diff --git a/CHANGELOG.md b/CHANGELOG.md
index 779ab50ae..6bd8eb12f 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -61,6 +61,7 @@ All notable changes to this project will be documented in this file.
 
 ### Changed
 
+-   #625 : Require all components of a `VectorFemSpace` to share the same `DomainDecomposition` object, see #615
 -   #527 : Pass a domain decomposition `ddm` and physical dimension `pdim` to `Geometry.__init__`; remove arguments `ncells`, `periodic`, `filename`, `comm` and `mpi_dims_mask`
 -   #527 : Use the domain decomposition of the mapping's space in `Geometry.from_discrete_mapping`; remove arguments `comm` and `mpi_dims_mask`
 -   #527 : Key `Geometry.mappings` by the names of the domain interiors
diff --git a/psydac/fem/tests/test_vector_spaces.py b/psydac/fem/tests/test_vector_spaces.py
index db813da75..26fe47f75 100644
--- a/psydac/fem/tests/test_vector_spaces.py
+++ b/psydac/fem/tests/test_vector_spaces.py
@@ -5,6 +5,7 @@
 #---------------------------------------------------------------------------#
 import pytest
 from numpy import linspace
+from mpi4py import MPI
 
 from psydac.fem.basic   import FemField
 from psydac.fem.splines import SplineSpace
@@ -143,6 +144,42 @@ def test_vector_space_3d():
     assert F.patch_fields == (F,)
     assert F.component_fields == F.fields
 
+#==============================================================================
+def make_tensor_space_2d(domain_decomposition: DomainDecomposition) -> TensorFemSpace:
+    """Create a 2D tensor-product spline space of degree 2 on the cells of the decomposition."""
+    spaces = [SplineSpace(2, grid=linspace(0., 1., n + 1), periodic=periodic)
+              for n, periodic in zip(domain_decomposition.ncells, domain_decomposition.periods)]
+    return TensorFemSpace(domain_decomposition, *spaces)
+
+def test_vector_space_shared_domain_decomposition():
+
+    ddm = DomainDecomposition([3, 5], [False, False])
+    V = VectorFemSpace(make_tensor_space_2d(ddm), make_tensor_space_2d(ddm))
+
+    assert all(W.domain_decomposition is ddm for W in V.spaces)
+
+def test_vector_space_different_domain_decompositions():
+
+    # Two decompositions are rejected even if equivalent (see #615)
+    Vx = make_tensor_space_2d(DomainDecomposition([3, 5], [False, False]))
+    Vy = make_tensor_space_2d(DomainDecomposition([3, 5], [False, False]))
+
+    with pytest.raises(AssertionError, match='same DomainDecomposition'):
+        VectorFemSpace(Vx, Vy)
+
+@pytest.mark.mpi(min_size=2)
+def test_vector_space_different_domain_decompositions_parallel():
+
+    # Decompositions along different axes give different local subdomains (see #615)
+    comm = MPI.COMM_WORLD
+    ncells = [2 * comm.size, 3 * comm.size]
+    Vx = make_tensor_space_2d(DomainDecomposition(ncells, [True, False], comm=comm, mpi_dims_mask=[True, False]))
+    Vy = make_tensor_space_2d(DomainDecomposition(ncells, [True, False], comm=comm, mpi_dims_mask=[False, True]))
+    assert Vx.local_domain != Vy.local_domain
+
+    with pytest.raises(AssertionError, match='same DomainDecomposition'):
+        VectorFemSpace(Vx, Vy)
+
 ###############################################
 if __name__ == '__main__':
 
diff --git a/psydac/fem/vector.py b/psydac/fem/vector.py
index 68ae3bb51..84595a779 100644
--- a/psydac/fem/vector.py
+++ b/psydac/fem/vector.py
@@ -70,6 +70,11 @@ def __init__(self, *spaces):
         for nc in zip(*ncells):
             assert len(set(nc)) == 1
 
+        # All spaces are defined on the same patch, hence they must share its decomposition
+        ddm = new_spaces[0].domain_decomposition
+        assert all(V.domain_decomposition is ddm for V in new_spaces), \
+            'All spaces must share the same DomainDecomposition object'
+
         # Compute the SymPDE symbolic space from the symbolic spaces of the input spaces
         symbolic_spaces = [V.symbolic_space for V in spaces]
         symbolic_space = reduce(lambda x, y: x * y, symbolic_spaces) if all(symbolic_spaces) else None