diff --git a/ot/lp/__init__.py b/ot/lp/__init__.py
index 752c5d2d7..cec98de27 100644
--- a/ot/lp/__init__.py
+++ b/ot/lp/__init__.py
@@ -237,6 +237,8 @@ def emd(a, b, M, numItermax=100000, log=False, center_dual=True, numThreads=1, c
 
     .. note:: An error will be raised if the vectors :math:`\mathbf{a}` and :math:`\mathbf{b}` do not sum to the same value.
 
+    .. note:: An error will be raided if the loss matrix :math:`\mathbf{M}` contains NaNs.
+
     Uses the algorithm proposed in :ref:`[1] <references-emd>`.
 
     Parameters
@@ -324,6 +326,9 @@ def emd(a, b, M, numItermax=100000, log=False, center_dual=True, numThreads=1, c
     # convert to numpy
     M, a, b = nx.to_numpy(M, a, b)
 
+    if np.isnan(M).any():
+        raise ValueError('The loss matrix should not contain NaN values.')
+  
     # ensure float64
     a = np.asarray(a, dtype=np.float64)
     b = np.asarray(b, dtype=np.float64)
@@ -502,6 +507,9 @@ def emd2(a, b, M, processes=1,
     # convert to numpy
     M, a, b = nx.to_numpy(M, a, b)
 
+    if np.isnan(M).any():
+        raise ValueError('The loss matrix should not contain NaN values.')
+
     a = np.asarray(a, dtype=np.float64)
     b = np.asarray(b, dtype=np.float64)
     M = np.asarray(M, dtype=np.float64, order='C')
diff --git a/test/gromov/test_gw.py b/test/gromov/test_gw.py
index 5b858f307..d8026352e 100644
--- a/test/gromov/test_gw.py
+++ b/test/gromov/test_gw.py
@@ -910,3 +910,18 @@ def test_fgw_barycenter(nx):
 
     np.testing.assert_allclose(C, Cb, atol=1e-06)
     np.testing.assert_allclose(X, Xb, atol=1e-06)
+
+
+# Related to issue 469
+def test_gromov2_nan_in_target_cost():
+    # GIVEN - a target cost matrix with a NaN value
+    source_cost = np.zeros((2, 2))
+    target_cost = np.ones((2, 2))
+    source_distribution = np.array([0.5, 0.5])
+    target_distribution = np.array([0.5, 0.5])
+
+    target_cost[0, 0] = np.nan
+
+    # WHEN - we call
+    with pytest.raises(ValueError, match='The loss matrix should not contain NaN values.'):
+        ot.gromov_wasserstein2(source_cost, target_cost, source_distribution, target_distribution)
diff --git a/test/test_ot.py b/test/test_ot.py
index a90321d5f..6096061cb 100644
--- a/test/test_ot.py
+++ b/test/test_ot.py
@@ -245,6 +245,11 @@ def test_emd_empty():
     np.testing.assert_allclose(w, 0)
 
 
+def test_emd_nan_in_loss_matrix():
+    with pytest.raises(ValueError, match='The loss matrix should not contain NaN values.'):
+        ot.emd([], [], [np.nan])
+
+
 def test_emd2_multi():
     n = 500  # nb bins