diff --git a/xrspatial/proximity.py b/xrspatial/proximity.py
index 35e331d8..b98fba68 100644
--- a/xrspatial/proximity.py
+++ b/xrspatial/proximity.py
@@ -735,6 +735,38 @@ def _process_proximity_line(
     return
 
 
+def _kdtree_query_lowest_index(tree, query_pts, p, max_distance):
+    """Nearest-target query that breaks ties by lowest target index.
+
+    ``cKDTree.query`` does not promise which of several equidistant targets
+    it returns, so allocation and direction can disagree with the brute-force
+    and CUDA backends on a tie. Target coordinates are stored in row-major
+    (flat-index) order, so the lowest target index is the lowest flat index --
+    the tie-break policy documented on ``allocation``/``direction``.
+
+    Query the two nearest targets; wherever they are equidistant, keep the one
+    with the smaller index. This resolves 2-way ties, which is what grid
+    geometry produces in practice. A pixel equidistant to three or more targets
+    relies on cKDTree returning the lower index among the rest, which it does
+    for the row-major target order used here but does not strictly promise.
+    """
+    n_targets = tree.n
+    if n_targets < 2:
+        return tree.query(query_pts, p=p, distance_upper_bound=max_distance)
+
+    dists2, idx2 = tree.query(query_pts, k=2, p=p,
+                              distance_upper_bound=max_distance)
+    dists = dists2[:, 0]
+    indices = idx2[:, 0]
+    # A tie exists where both neighbours are finite and equidistant. Prefer the
+    # smaller index in that case so the result is independent of cKDTree's
+    # internal traversal order.
+    tied = np.isfinite(dists2[:, 1]) & (dists2[:, 1] == dists)
+    if tied.any():
+        indices = np.where(tied, np.minimum(idx2[:, 0], idx2[:, 1]), indices)
+    return dists, indices
+
+
 def _kdtree_chunk_fn(block, y_coords_1d, x_coords_1d,
                      tree, block_info, max_distance, p,
                      process_mode, target_vals, target_coords):
@@ -751,8 +783,8 @@ def _kdtree_chunk_fn(block, y_coords_1d, x_coords_1d,
     yy, xx = np.meshgrid(chunk_ys, chunk_xs, indexing='ij')
     query_pts = np.column_stack([yy.ravel(), xx.ravel()])
 
-    dists, indices = tree.query(query_pts, p=p,
-                                distance_upper_bound=max_distance)
+    dists, indices = _kdtree_query_lowest_index(
+        tree, query_pts, p, max_distance)
 
     n_targets = len(target_vals)
     oob = indices >= n_targets
@@ -979,7 +1011,7 @@ def _tiled_chunk_query(raster, iy, ix, y_coords, x_coords,
 
         tree = cKDTree(target_coords)
         ub = max_distance if np.isfinite(max_distance) else np.inf
-        dists, indices = tree.query(query_pts, p=p, distance_upper_bound=ub)
+        dists, indices = _kdtree_query_lowest_index(tree, query_pts, p, ub)
 
         n_targets = len(target_vals)
         oob = indices >= n_targets
@@ -1374,6 +1406,22 @@ def _process_numpy(img, x_coords, y_coords):
                 img, x_coords, y_coords, target_values,
                 np.float32(max_distance), distance_metric, process_mode,
             )
+        # ALLOCATION and DIRECTION pick a single target per pixel, so a tie
+        # between two equidistant targets must resolve the same way on every
+        # backend. The line-sweep breaks ties as a side effect of its
+        # four-pass propagation order, which disagrees with the brute-force
+        # and CUDA kernels. Route those modes through the brute-force search,
+        # which keeps the lowest-flat-index target on a tie (see the
+        # `allocation`/`direction` docstrings). Brute force is O(N*T) versus
+        # the line-sweep's O(N); the slower scan is a deliberate trade for a
+        # tie-break that matches every other backend. PROXIMITY only returns
+        # the distance, which is identical for tied targets, so the faster
+        # line-sweep stays in use there.
+        if process_mode in (ALLOCATION, DIRECTION):
+            return _process_numpy_bruteforce(
+                img, x_coords, y_coords, target_values,
+                np.float32(max_distance), distance_metric, process_mode,
+            )
         return _process_numpy_linesweep(img, x_coords, y_coords)
 
     def _process_dask(raster, xs, ys):
@@ -1680,6 +1728,13 @@ def allocation(
     `allocation` chunk by chunk by expanding the chunk's borders to cover
     the `max_distance`.
 
+    Tie-breaking: when two or more targets are exactly equidistant from a
+    pixel, the target with the lowest flat (row-major) index wins, i.e. the
+    first target encountered when scanning the raster top-to-bottom and
+    left-to-right. This policy is identical across all backends (numpy, cupy,
+    dask+numpy, dask+cupy), so the allocated value is deterministic regardless
+    of which backend computes it.
+
     Parameters
     ----------
     raster : xr.DataArray or xr.Dataset
@@ -1831,6 +1886,13 @@ def direction(
     proximity direction chunk by chunk by expanding the chunk's borders
     to cover the `max_distance`.
 
+    Tie-breaking: when two or more targets are exactly equidistant from a
+    pixel, the direction is computed toward the target with the lowest flat
+    (row-major) index, i.e. the first target encountered when scanning the
+    raster top-to-bottom and left-to-right. This policy is identical across
+    all backends (numpy, cupy, dask+numpy, dask+cupy), so the reported
+    direction is deterministic regardless of which backend computes it.
+
     Parameters
     ----------
     raster : xr.DataArray or xr.Dataset
diff --git a/xrspatial/tests/test_proximity.py b/xrspatial/tests/test_proximity.py
index 726e82f8..e012a811 100644
--- a/xrspatial/tests/test_proximity.py
+++ b/xrspatial/tests/test_proximity.py
@@ -535,6 +535,58 @@ def test_proximity_dask_kdtree_with_target_values():
     )
 
 
+# ---------------------------------------------------------------------------
+# Tie-breaking: when two targets are equidistant, every backend must pick the
+# same one. The documented policy is "lowest flat (row-major) index wins".
+# ---------------------------------------------------------------------------
+
+@pytest.fixture
+def tie_break_raster_data():
+    # Targets at (1, 0)=1 and (1, 2)=2. The whole centre column is equidistant
+    # to both. Target 1 sits at flat index 3, target 2 at flat index 5, so the
+    # lowest-flat-index policy allocates the centre column to 1.
+    return np.array([[0., 0., 0.],
+                     [1., 0., 2.],
+                     [0., 0., 0.]], dtype=np.float64)
+
+
+@pytest.fixture
+def tie_break_expected_allocation():
+    return np.array([[1., 1., 2.],
+                     [1., 1., 2.],
+                     [1., 1., 2.]], dtype=np.float32)
+
+
+@pytest.mark.parametrize("backend", ['numpy', 'dask+numpy', 'cupy', 'dask+cupy'])
+def test_allocation_tie_break_lowest_flat_index(
+        backend, tie_break_raster_data, tie_break_expected_allocation):
+    raster = create_test_raster(
+        tie_break_raster_data, backend=backend, dims=['lat', 'lon'],
+        chunks=(1, 1),
+    )
+    result = allocation(raster, x='lon', y='lat')
+    general_output_checks(
+        raster, result, tie_break_expected_allocation, verify_dtype=True,
+    )
+
+
+@pytest.mark.parametrize("backend", ['numpy', 'dask+numpy', 'cupy', 'dask+cupy'])
+def test_direction_tie_break_matches_numpy(backend, tie_break_raster_data):
+    # The numpy backend is the reference. Pin every other backend to it so the
+    # direction angle chosen on a tie stays identical across backends.
+    numpy_raster = create_test_raster(
+        tie_break_raster_data, backend='numpy', dims=['lat', 'lon'],
+    )
+    expected = direction(numpy_raster, x='lon', y='lat').data
+
+    raster = create_test_raster(
+        tie_break_raster_data, backend=backend, dims=['lat', 'lon'],
+        chunks=(1, 1),
+    )
+    result = direction(raster, x='lon', y='lat')
+    general_output_checks(raster, result, expected)
+
+
 @pytest.mark.skipif(da is None, reason="dask is not installed")
 def test_proximity_dask_kdtree_no_targets():
     """No target pixels found → result is all NaN."""
@@ -704,6 +756,40 @@ def test_proximity_dask_kdtree_tiled_manhattan():
     )
 
 
+@pytest.mark.skipif(da is None, reason="dask is not installed")
+def test_allocation_tie_break_tiled_path():
+    """The eager tiled KDTree fallback obeys the lowest-flat-index tie-break."""
+    data = np.array([[0., 0., 0.],
+                     [1., 0., 2.],
+                     [0., 0., 0.]], dtype=np.float64)
+    _lon = np.array([0., 1., 2.])
+    _lat = np.array([2., 1., 0.])
+    raster = xr.DataArray(data, dims=['lat', 'lon'])
+    raster['lon'] = _lon
+    raster['lat'] = _lat
+    raster.data = da.from_array(data, chunks=(1, 1))
+
+    # Force the eager tiled KDTree path (see _force_tiled_proximity for the
+    # counter semantics): tiny cache budget, force the tiled decision, then a
+    # large value so the result-size guard passes.
+    call_count = [0]
+
+    def _small_then_large():
+        call_count[0] += 1
+        if call_count[0] <= 2:
+            return 1
+        return 10 * 1024 ** 3
+
+    with patch('xrspatial.proximity._available_memory_bytes',
+               side_effect=_small_then_large):
+        result = allocation(raster, x='lon', y='lat')
+
+    expected = np.array([[1., 1., 2.],
+                         [1., 1., 2.],
+                         [1., 1., 2.]], dtype=np.float32)
+    np.testing.assert_array_equal(result.values, expected)
+
+
 @pytest.mark.skipif(da is None, reason="dask is not installed")
 def test_proximity_dask_kdtree_tiled_single_target():
     """One target in a corner, many chunks → exercises max ring expansion."""