diff --git a/src/somd2/runner/_repex.py b/src/somd2/runner/_repex.py
index 986f439..9aba785 100644
--- a/src/somd2/runner/_repex.py
+++ b/src/somd2/runner/_repex.py
@@ -72,6 +72,8 @@ def __init__(self, system, lambdas, num_gpus, dynamics_kwargs):
         self._states = _np.array(range(len(lambdas)))
         self._openmm_states = [None] * len(lambdas)
         self._openmm_volumes = [None] * len(lambdas)
+        self._num_proposed = _np.matrix(_np.zeros((len(lambdas), len(lambdas))))
+        self._num_accepted = _np.matrix(_np.zeros((len(lambdas), len(lambdas))))
 
         # Copy the dynamics keyword arguments.
         dynamics_kwargs = dynamics_kwargs.copy()
@@ -185,6 +187,18 @@ def mix_states(self):
                 _logger.debug(f"Replica {i} seeded from state {state}")
                 self._dynamics[i]._d._omm_mols.setState(self._openmm_states[state])
 
+    def get_proposed(self):
+        """
+        Return the number of proposed swaps between replicas.
+        """
+        return self._num_proposed
+
+    def get_accepted(self):
+        """
+        Return the number of accepted swaps between replicas.
+        """
+        return self._num_accepted
+
 
 class RepexRunner(_RunnerBase):
     """
@@ -263,6 +277,9 @@ def __init__(self, system, config):
         else:
             self._start_block = 0
 
+        # Store the name of the replica exchange swap acceptance matrix.
+        self._repex_matrix = self._config.output_directory / "repex_matrix.txt"
+
         from threading import Lock
 
         # Create a lock to guard the dynamics cache.
@@ -412,14 +429,25 @@ def run(self):
                     self._mix_replicas(
                         self._config.num_lambda,
                         energy_matrix,
+                        self._dynamics_cache.get_proposed(),
+                        self._dynamics_cache.get_accepted(),
                     )
                 )
                 self._dynamics_cache.mix_states()
 
-                # Update the block number.
+                # This is a checkpoint cycle.
                 if is_checkpoint:
+                    # Update the block number.
                     block += 1
 
+                    # Save the replica exchange swap acceptance matrix.
+                    _np.savetxt(
+                        self._repex_matrix,
+                        self._dynamics_cache.get_accepted()
+                        / self._dynamics_cache.get_proposed(),
+                        fmt="%.5f",
+                    )
+
         # Record the end time.
         end = time()
 
@@ -593,7 +621,7 @@ def _assemble_results(self, results):
 
     @staticmethod
     @_njit
-    def _mix_replicas(num_replicas, energy_matrix):
+    def _mix_replicas(num_replicas, energy_matrix, proposed, accepted):
         """
         Mix the replicas.
 
@@ -628,6 +656,9 @@ def _mix_replicas(num_replicas, energy_matrix):
             state_i = states[replica_i]
             state_j = states[replica_j]
 
+            # Record that we have proposed a swap.
+            proposed[state_i, state_j] += 1
+
             # Get the energies.
             energy_ii = energy_matrix[replica_i, state_i]
             energy_jj = energy_matrix[replica_j, state_j]
@@ -639,7 +670,10 @@ def _mix_replicas(num_replicas, energy_matrix):
 
             # Accept the swap and update the states.
             if log_p_swap >= 0 or _np.random.rand() < _np.exp(log_p_swap):
+                # Swap the states.
                 states[replica_i] = state_j
                 states[replica_j] = state_i
+                # Record the swap.
+                accepted[state_i, state_j] += 1
 
         return states