diff --git a/spatialmath/baseposematrix.py b/spatialmath/baseposematrix.py
index 87071df3..9d4d49cc 100644
--- a/spatialmath/baseposematrix.py
+++ b/spatialmath/baseposematrix.py
@@ -1350,6 +1350,20 @@ def __imul__(left, right):  # noqa
         """
         return left.__mul__(right)
 
+    def __imatmul__(left, right):  # noqa
+        """
+        Overloaded ``@=`` operator (superclass method)
+
+        :return: Product of two operands with normalization
+        :rtype: Pose instance or NumPy array
+        :raises ValueError: for incompatible arguments
+
+        - ``X @= Y`` compounds the poses ``X`` and ``Y`` and places the normalized result in ``X``
+
+        :seealso: ``__imul__`` :meth:`__matmul__`
+        """
+        return left.__matmul__(right)
+
     def __truediv__(left, right):  # pylint: disable=no-self-argument
         """
         Overloaded ``/`` operator (superclass method)
diff --git a/spatialmath/quaternion.py b/spatialmath/quaternion.py
index 2994b6e6..9093f5f6 100644
--- a/spatialmath/quaternion.py
+++ b/spatialmath/quaternion.py
@@ -666,6 +666,40 @@ def __imul__(
         """
         return left.__mul__(right)
 
+    def __imatmul__(
+        left, right: Quaternion
+    ) -> Quaternion:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
+        """
+        Overloaded ``@=`` operator
+
+        :return: product
+        :rtype: Quaternion
+        :raises: ValueError
+
+        ``q1 @= q2`` sets ``q1 := qnorm(q1 * q2)``. Only meaningful for
+        ``UnitQuaternion``, which is the only subclass defining ``__matmul__``
+        (with normalization) that this delegates to; on a plain ``Quaternion``
+        this raises the same ``TypeError`` that ``q1 @ q2`` would.
+
+        Example:
+
+        .. runblock:: pycon
+
+            >>> from spatialmath import UnitQuaternion
+            >>> q = UnitQuaternion.Eul([0.1, 0.2, 0.3])
+            >>> q @= UnitQuaternion.Eul([0.3, 0.4, 0.5])
+            >>> print(q)
+
+
+        :seealso: :func:`__matmul__`
+        """
+        # NOT left.__matmul__(right): Quaternion itself has no __matmul__
+        # (only UnitQuaternion defines one), and calling the dunder
+        # directly as a plain attribute skips Python's normal operator
+        # fallback, raising a confusing AttributeError instead of the
+        # TypeError that `left @ right` raises consistently.
+        return left @ right
+
     def __pow__(self, n: int) -> Quaternion:
         """
         Overloaded ``**`` operator
@@ -1883,8 +1917,6 @@ def __matmul__(
         - ``q1 @ q2`` is the Hamilton product of ``q1`` and ``q2``, both unit
           quaternions, followed by explicit normalization.
 
-        - `` q1 @= q2`` as above.
-
         .. note:: This operator is functionally equivalent to ``*`` but is more
             costly.  It is useful for cases where a pose is incrementally update
             over many cycles.
diff --git a/tests/test_pose3d.py b/tests/test_pose3d.py
index cdb80fbd..40b0a914 100755
--- a/tests/test_pose3d.py
+++ b/tests/test_pose3d.py
@@ -419,6 +419,11 @@ def test_arith(self):
         self.assertIsInstance(R, SO3)
         array_compare(R, rotx(pi / 2))
 
+        R = SO3()
+        R @= SO3.Rx(pi / 2)
+        self.assertIsInstance(R, SO3)
+        array_compare(R, rotx(pi / 2))
+
         R = SO3()
         R *= 2
         self.assertNotIsInstance(R, SO3)
@@ -1078,6 +1083,13 @@ def test_arith(self):
             T, np.array([[0, 0, 1, 1], [0, 1, 0, 2], [-1, 0, 0, 3], [0, 0, 0, 1]])
         )
 
+        T = SE3(1, 2, 3)
+        T @= SE3.Ry(pi / 2)
+        self.assertIsInstance(T, SE3)
+        array_compare(
+            T, np.array([[0, 0, 1, 1], [0, 1, 0, 2], [-1, 0, 0, 3], [0, 0, 0, 1]])
+        )
+
         T = SE3()
         T *= 2
         self.assertNotIsInstance(T, SE3)
diff --git a/tests/test_quaternion.py b/tests/test_quaternion.py
index 75d31b7c..24c264ef 100644
--- a/tests/test_quaternion.py
+++ b/tests/test_quaternion.py
@@ -507,6 +507,11 @@ def test_matmul(self):
             UnitQuaternion([ry * rx, rz * ry, rx * rz]),
         )
 
+        # @= is @ as an augmented assignment, not *=
+        q = rx
+        q @= ry
+        qcompare(q, rx @ ry)
+
     # def multiply_test_normalized(self):
 
     #     vx = [1, 0, 0]; vy = [0, 1, 0]; vz = [0, 0, 1]
@@ -949,6 +954,14 @@ def test_multiply(self):
         q *= q2
         qcompare(q, [-12, 6, 24, 12])
 
+        # plain Quaternion has no @ (only UnitQuaternion normalizes via @),
+        # so @= must fail the same way @ does, not silently fall back to *=
+        with self.assertRaises(TypeError):
+            q1 @ q2
+        with self.assertRaises(TypeError):
+            q = q1
+            q @= q2
+
         # vector x vector
         qcompare(
             Quaternion([q1, u, q2, u, q3, u]) * Quaternion([u, q1, u, q2, u, q3]),