diff --git a/proto/message.proto b/proto/message.proto
index ff5bfd7..92ae378 100644
--- a/proto/message.proto
+++ b/proto/message.proto
@@ -45,8 +45,9 @@ message LemmaProto {
 }
 
 message AgreementProto {
+  uint32 epoch = 1;
   oneof payload {
-    bool bval = 1;
-    bool aux = 2;
+    bool bval = 2;
+    bool aux = 3;
   }
 }
\ No newline at end of file
diff --git a/src/agreement.rs b/src/agreement.rs
index 0c733be..95b7655 100644
--- a/src/agreement.rs
+++ b/src/agreement.rs
@@ -1,26 +1,61 @@
 //! Binary Byzantine agreement protocol from a common coin protocol.
 
-use proto::AgreementMessage;
-use std::collections::{BTreeSet, VecDeque};
+use std::collections::{BTreeMap, BTreeSet, HashMap, VecDeque};
+use std::hash::Hash;
 
-#[derive(Default)]
-pub struct Agreement {
+use proto::AgreementMessage;
+
+pub struct Agreement<NodeUid> {
+    /// The UID of the corresponding node.
+    uid: NodeUid,
+    num_nodes: usize,
+    num_faulty_nodes: usize,
+    epoch: u32,
     input: Option<bool>,
-    _bin_values: BTreeSet<bool>,
+    /// Bin values. Reset on every epoch update.
+    bin_values: BTreeSet<bool>,
+    /// Values received in BVAL messages. Reset on every epoch update.
+    received_bval: HashMap<NodeUid, BTreeSet<bool>>,
+    /// Sent BVAL values. Reset on every epoch update.
+    sent_bval: BTreeSet<bool>,
+    /// Values received in AUX messages. Reset on every epoch update.
+    received_aux: HashMap<NodeUid, BTreeSet<bool>>,
+    /// All the output values in all epochs.
+    outputs: BTreeMap<u32, bool>,
+    /// Termination flag.
+    terminated: bool,
 }
 
-impl Agreement {
-    pub fn new() -> Self {
+impl<NodeUid: Clone + Eq + Hash> Agreement<NodeUid> {
+    pub fn new(uid: NodeUid, num_nodes: usize) -> Self {
+        let num_faulty_nodes = (num_nodes - 1) / 3;
+
         Agreement {
+            uid,
+            num_nodes,
+            num_faulty_nodes,
+            epoch: 0,
             input: None,
-            _bin_values: BTreeSet::new(),
+            bin_values: BTreeSet::new(),
+            received_bval: HashMap::new(),
+            sent_bval: BTreeSet::new(),
+            received_aux: HashMap::new(),
+            outputs: BTreeMap::new(),
+            terminated: false,
         }
     }
 
+    /// Algorithm has terminated.
+    pub fn terminated(&self) -> bool {
+        self.terminated
+    }
+
     pub fn set_input(&mut self, input: bool) -> AgreementMessage {
         self.input = Some(input);
+        // Receive the BVAL message locally.
+        update_map_of_sets(&mut self.received_bval, self.uid.clone(), input);
         // Multicast BVAL
-        AgreementMessage::BVal(input)
+        AgreementMessage::BVal((self.epoch, input))
     }
 
     pub fn has_input(&self) -> bool {
@@ -28,12 +63,170 @@ impl Agreement {
     }
 
     /// Receive input from a remote node.
+    ///
+    /// Outputs an optional agreement result and a queue of agreement messages
+    /// to remote nodes. There can be up to 2 messages.
     pub fn on_input(
-        &self,
-        _message: &AgreementMessage,
-    ) -> Result<VecDeque<AgreementMessage>, Error> {
-        Err(Error::NotImplemented)
+        &mut self,
+        uid: NodeUid,
+        message: &AgreementMessage,
+    ) -> Result<(Option<bool>, VecDeque<AgreementMessage>), Error> {
+        let mut outgoing = VecDeque::new();
+
+        match *message {
+            AgreementMessage::BVal((epoch, b)) if epoch == self.epoch => {
+                update_map_of_sets(&mut self.received_bval, uid, b);
+                let count_bval = self.received_bval.iter().fold(0, |count, (_, values)| {
+                    if values.contains(&b) {
+                        count + 1
+                    } else {
+                        count
+                    }
+                });
+
+                // upon receiving BVAL_r(b) messages from 2f + 1 nodes,
+                // bin_values_r := bin_values_r ∪ {b}
+                if count_bval == 2 * self.num_faulty_nodes + 1 {
+                    self.bin_values.insert(b);
+
+                    // wait until bin_values_r /= 0, then multicast AUX_r(w)
+                    // where w ∈ bin_values_r
+                    outgoing.push_back(AgreementMessage::Aux((self.epoch, b)));
+                    // Receive the AUX message locally.
+                    update_map_of_sets(&mut self.received_aux, self.uid.clone(), b);
+
+                    let coin_result = self.try_coin();
+                    if let Some(output_message) = coin_result.1 {
+                        outgoing.push_back(output_message);
+                    }
+                    Ok((coin_result.0, outgoing))
+                }
+                // upon receiving BVAL_r(b) messages from f + 1 nodes, if
+                // BVAL_r(b) has not been sent, multicast BVAL_r(b)
+                else if count_bval == self.num_faulty_nodes + 1 && !self.sent_bval.contains(&b) {
+                    outgoing.push_back(AgreementMessage::BVal((self.epoch, b)));
+                    // Receive the BVAL message locally.
+                    update_map_of_sets(&mut self.received_bval, self.uid.clone(), b);
+                    Ok((None, outgoing))
+                } else {
+                    Ok((None, outgoing))
+                }
+            }
+
+            AgreementMessage::Aux((_epoch, b)) => {
+                update_map_of_sets(&mut self.received_aux, uid, b);
+                if !self.bin_values.is_empty() {
+                    let coin_result = self.try_coin();
+                    if let Some(output_message) = coin_result.1 {
+                        outgoing.push_back(output_message);
+                    }
+                    Ok((coin_result.0, outgoing))
+                } else {
+                    Ok((None, outgoing))
+                }
+            }
+
+            _ => {
+                // Epoch does not match. Ignore the message.
+                Ok((None, outgoing))
+            }
+        }
     }
+
+    /// AUX_r messages such that the set of values carried by those messages is
+    /// a subset of bin_values_r. Outputs this subset.
+    ///
+    /// FIXME: Clarify whether the values of AUX messages should be the same or
+    /// not. It is assumed in `count_aux` that they can differ.
+    fn count_aux(&self) -> (usize, BTreeSet<bool>) {
+        let vals = BTreeSet::new();
+        (
+            self.received_aux.iter().fold(0, |count, (_, values)| {
+                if values.is_subset(&self.bin_values) {
+                    vals.union(values);
+                    count + 1
+                } else {
+                    count
+                }
+            }),
+            vals,
+        )
+    }
+
+    /// Wait until at least (N − f) AUX_r messages have been received, such that
+    /// the set of values carried by these messages, vals, are a subset of
+    /// bin_values_r (note that bin_values_r may continue to change as BVAL_r
+    /// messages are received, thus this condition may be triggered upon arrival
+    /// of either an AUX_r or a BVAL_r message).
+    ///
+    /// `try_coin` output an optional combination of the agreement value and the
+    /// agreement broadcast message.
+    fn try_coin(&mut self) -> (Option<bool>, Option<AgreementMessage>) {
+        let (count_aux, vals) = self.count_aux();
+        if count_aux >= self.num_nodes - self.num_faulty_nodes {
+            // FIXME: Implement the Common Coin algorithm. At the moment the
+            // coin value is constant `true`.
+            let coin: u64 = 1;
+
+            let coin2 = coin % 2 != 0;
+
+            // Check the termination condition: "continue looping until both a
+            // value b is output in some round r, and the value Coin_r' = b for
+            // some round r' > r."
+            self.terminated = self.terminated || self.outputs.values().any(|b| *b == coin2);
+
+            // Prepare to start the next epoch.
+            self.bin_values.clear();
+
+            if vals.len() == 1 {
+                let mut message = None;
+                // NOTE: `vals` has exactly one element due to `vals.len() == 1`
+                let output: Vec<Option<bool>> = vals.into_iter()
+                    .take(1)
+                    .map(|b| {
+                        message = Some(self.set_input(b));
+
+                        if b == coin2 {
+                            // Record the output to perform a termination check later.
+                            self.outputs.insert(self.epoch, b);
+                            // Output the agreement value.
+                            Some(b)
+                        } else {
+                            // Don't output a value.
+                            None
+                        }
+                    })
+                    .collect();
+                // Start the next epoch.
+                self.epoch += 1;
+                (output[0], message)
+            } else {
+                // Start the next epoch.
+                self.epoch += 1;
+                (None, Some(self.set_input(coin2)))
+            }
+        } else {
+            // Continue waiting for the (N - f) AUX messages.
+            (None, None)
+        }
+    }
+}
+
+// Insert an element into a hash map of sets of values of type `Elt`.
+fn update_map_of_sets<Key, Elt>(map: &mut HashMap<Key, BTreeSet<Elt>>, key: Key, elt: Elt)
+where
+    Key: Eq + Hash,
+    Elt: Copy + Ord,
+{
+    map.entry(key)
+        .and_modify(|values| {
+            values.insert(elt);
+        })
+        .or_insert({
+            let mut values = BTreeSet::new();
+            values.insert(elt);
+            values
+        });
 }
 
 #[derive(Clone, Debug)]
diff --git a/src/common_subset.rs b/src/common_subset.rs
index d92c5d4..55f85e0 100644
--- a/src/common_subset.rs
+++ b/src/common_subset.rs
@@ -43,15 +43,15 @@ pub struct CommonSubset<NodeUid: Eq + Hash + Ord> {
     uid: NodeUid,
     num_nodes: usize,
     num_faulty_nodes: usize,
-    agreement_true_outputs: HashSet<NodeUid>,
     broadcast_instances: HashMap<NodeUid, Broadcast<NodeUid>>,
-    agreement_instances: HashMap<NodeUid, Agreement>,
+    agreement_instances: HashMap<NodeUid, Agreement<NodeUid>>,
     broadcast_results: HashMap<NodeUid, ProposedValue>,
     agreement_results: HashMap<NodeUid, bool>,
 }
 
 impl<NodeUid: Clone + Debug + Display + Eq + Hash + Ord> CommonSubset<NodeUid> {
-    pub fn new(uid: NodeUid, all_uids: &HashSet<NodeUid>, num_nodes: usize) -> Result<Self, Error> {
+    pub fn new(uid: NodeUid, all_uids: &HashSet<NodeUid>) -> Result<Self, Error> {
+        let num_nodes = all_uids.len();
         let num_faulty_nodes = (num_nodes - 1) / 3;
 
         // Create all broadcast instances.
@@ -68,18 +68,17 @@ impl<NodeUid: Clone + Debug + Display + Eq + Hash + Ord> CommonSubset<NodeUid> {
         }
 
         // Create all agreement instances.
-        let mut agreement_instances: HashMap<NodeUid, Agreement> = HashMap::new();
+        let mut agreement_instances: HashMap<NodeUid, Agreement<NodeUid>> = HashMap::new();
         for uid0 in all_uids {
-            agreement_instances.insert(uid0.clone(), Agreement::new());
+            agreement_instances.insert(uid0.clone(), Agreement::new(uid0.clone(), num_nodes));
         }
 
         Ok(CommonSubset {
             uid,
             num_nodes,
             num_faulty_nodes,
-            agreement_true_outputs: HashSet::new(),
             broadcast_instances,
-            agreement_instances: HashMap::new(),
+            agreement_instances,
             broadcast_results: HashMap::new(),
             agreement_results: HashMap::new(),
         })
@@ -109,7 +108,7 @@ impl<NodeUid: Clone + Debug + Display + Eq + Hash + Ord> CommonSubset<NodeUid> {
         &mut self,
         uid: &NodeUid,
     ) -> Result<Option<AgreementMessage>, Error> {
-        if let Some(agreement_instance) = self.agreement_instances.get_mut(uid) {
+        if let Some(agreement_instance) = self.agreement_instances.get_mut(&uid) {
             if !agreement_instance.has_input() {
                 Ok(Some(agreement_instance.set_input(true)))
             } else {
@@ -146,11 +145,35 @@ impl<NodeUid: Clone + Debug + Display + Eq + Hash + Ord> CommonSubset<NodeUid> {
                 }
                 input_result
             }
-            Input::Agreement(_uid, _message) => {
-                // FIXME: send the message to the Agreement instance and
-                // conditionally call `on_agreement_output`
 
-                Err(Error::NotImplemented)
+            Input::Agreement(uid, amessage) => {
+                // The result defaults to error.
+                let mut result = Err(Error::NoSuchAgreementInstance);
+
+                // FIXME: send the message to the Agreement instance and
+                if let Some(mut agreement_instance) = self.agreement_instances.get_mut(&uid) {
+                    // Optional output of agreement and outgoing agreement
+                    // messages to remote nodes.
+                    result = if agreement_instance.terminated() {
+                        // This instance has terminated and does not accept input.
+                        Ok((None, VecDeque::new()))
+                    } else {
+                        agreement_instance
+                            .on_input(uid.clone(), &amessage)
+                            .map_err(Error::from)
+                    }
+                }
+
+                if let Ok((output, mut outgoing)) = result {
+                    if let Some(b) = output {
+                        outgoing.append(&mut self.on_agreement_result(uid, b));
+                    }
+                    Ok(outgoing.into_iter().map(Output::Agreement).collect())
+                } else {
+                    // error
+                    result
+                        .map(|(_, messages)| messages.into_iter().map(Output::Agreement).collect())
+                }
             }
         }
     }
@@ -166,9 +189,14 @@ impl<NodeUid: Clone + Debug + Display + Eq + Hash + Ord> CommonSubset<NodeUid> {
         // Upon delivery of value 1 from at least N − f instances of BA, provide
         // input 0 to each instance of BA that has not yet been provided input.
         if result {
-            self.agreement_true_outputs.insert(uid);
+            self.agreement_results.insert(uid, result);
+            let results1: Vec<bool> = self.agreement_results
+                .iter()
+                .map(|(_, v)| *v)
+                .filter(|b| *b)
+                .collect();
 
-            if self.agreement_true_outputs.len() >= self.num_nodes - self.num_faulty_nodes {
+            if results1.len() >= self.num_nodes - self.num_faulty_nodes {
                 let instances = &mut self.agreement_instances;
                 for (_uid0, instance) in instances.iter_mut() {
                     if !instance.has_input() {
@@ -222,6 +250,7 @@ pub enum Error {
     UnexpectedMessage,
     NotImplemented,
     NoSuchBroadcastInstance,
+    NoSuchAgreementInstance,
     Broadcast(broadcast::Error),
     Agreement(agreement::Error),
 }
diff --git a/src/proto/mod.rs b/src/proto/mod.rs
index ba5e2a0..7163d8d 100644
--- a/src/proto/mod.rs
+++ b/src/proto/mod.rs
@@ -67,10 +67,12 @@ impl<'a, T: AsRef<[u8]>> fmt::Debug for HexProof<'a, T> {
 }
 
 /// Messages sent during the binary Byzantine agreement stage.
-#[derive(Copy, Clone, Debug, PartialEq)]
+#[derive(Clone, Debug, PartialEq, Eq, PartialOrd, Ord)]
 pub enum AgreementMessage {
-    BVal(bool),
-    Aux(bool),
+    /// BVAL message with an epoch.
+    BVal((u32, bool)),
+    /// AUX message with an epoch.
+    Aux((u32, bool)),
 }
 
 impl<T: Send + Sync + AsRef<[u8]> + From<Vec<u8>>> Message<T> {
@@ -175,8 +177,14 @@ impl AgreementMessage {
     pub fn into_proto(self) -> AgreementProto {
         let mut p = AgreementProto::new();
         match self {
-            AgreementMessage::BVal(b) => p.set_bval(b),
-            AgreementMessage::Aux(b) => p.set_aux(b),
+            AgreementMessage::BVal((e, b)) => {
+                p.set_epoch(e);
+                p.set_bval(b);
+            }
+            AgreementMessage::Aux((e, b)) => {
+                p.set_epoch(e);
+                p.set_aux(b);
+            }
         }
         p
     }
@@ -184,10 +192,11 @@ impl AgreementMessage {
     // TODO: Re-enable lint once implemented.
     #[cfg_attr(feature = "cargo-clippy", allow(needless_pass_by_value))]
     pub fn from_proto(mp: AgreementProto) -> Option<Self> {
+        let epoch = mp.get_epoch();
         if mp.has_bval() {
-            Some(AgreementMessage::BVal(mp.get_bval()))
+            Some(AgreementMessage::BVal((epoch, mp.get_bval())))
         } else if mp.has_aux() {
-            Some(AgreementMessage::Aux(mp.get_aux()))
+            Some(AgreementMessage::Aux((epoch, mp.get_aux())))
         } else {
             None
         }