diff --git a/CHANGELOG.md b/CHANGELOG.md
index c9db0d9b..bfd051c0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,11 @@ changelog does not include internal changes that do not affect the user.
 
 ## [Unreleased]
 
+### Fixed
+
+- Added a fallback for when the inner optimization of `NashMTL` fails (which can happen for example
+  on the matrix [[0., 0.], [0., 1.]]).
+
 ## [0.9.0] - 2026-02-24
 
 ### Added
diff --git a/src/torchjd/aggregation/_nash_mtl.py b/src/torchjd/aggregation/_nash_mtl.py
index 06e1293d..a20be617 100644
--- a/src/torchjd/aggregation/_nash_mtl.py
+++ b/src/torchjd/aggregation/_nash_mtl.py
@@ -158,9 +158,10 @@ def _solve_optimization(self, gtg: np.ndarray) -> np.ndarray:
 
             try:
                 self.prob.solve(solver=cp.ECOS, warm_start=True, max_iters=100)
-            except SolverError:
-                # On macOS, this can happen with: Solver 'ECOS' failed.
+            except (SolverError, ValueError):
+                # On macOS, SolverError can happen with: Solver 'ECOS' failed.
                 # No idea why. The corresponding matrix is of shape [9, 11] with rank 5.
+                # ValueError happens with for example matrix [[0., 0.], [0., 1.]].
                 # Maybe other exceptions can happen in other cases.
                 self.alpha_param.value = self.prvs_alpha_param.value
 
diff --git a/tests/unit/aggregation/test_nash_mtl.py b/tests/unit/aggregation/test_nash_mtl.py
index a1200d46..d82fca41 100644
--- a/tests/unit/aggregation/test_nash_mtl.py
+++ b/tests/unit/aggregation/test_nash_mtl.py
@@ -1,7 +1,7 @@
 from pytest import mark
 from torch import Tensor
 from torch.testing import assert_close
-from utils.tensors import ones_, randn_
+from utils.tensors import ones_, randn_, tensor_
 
 try:
     from torchjd.aggregation import NashMTL
@@ -19,6 +19,10 @@ def _make_aggregator(matrix: Tensor) -> NashMTL:
 
 
 standard_pairs = [(_make_aggregator(matrix), matrix) for matrix in nash_mtl_matrices]
+edge_case_matrices = [
+    tensor_([[0.0, 0.0], [0.0, 1.0]])  # This leads to a (caught) ValueError in _solve_optimization.
+]
+edge_case_pairs = [(_make_aggregator(matrix), matrix) for matrix in edge_case_matrices]
 requires_grad_pairs = [(NashMTL(n_tasks=3), ones_(3, 5, requires_grad=True))]
 
 
@@ -27,8 +31,13 @@ def _make_aggregator(matrix: Tensor) -> NashMTL:
 @mark.filterwarnings(
     "ignore:Solution may be inaccurate.",
     "ignore:You are solving a parameterized problem that is not DPP.",
+    "ignore:divide by zero encountered in divide",
+    "ignore:divide by zero encountered in true_divide",
+    "ignore:overflow encountered in divide",
+    "ignore:overflow encountered in true_divide",
+    "ignore:invalid value encountered in matmul",
 )
-@mark.parametrize(["aggregator", "matrix"], standard_pairs)
+@mark.parametrize(["aggregator", "matrix"], standard_pairs + edge_case_pairs)
 def test_expected_structure(aggregator: NashMTL, matrix: Tensor) -> None:
     assert_expected_structure(aggregator, matrix)