diff --git a/tests/test_api_link.py b/tests/test_api_link.py
index ebe0e90fb..1e808687d 100644
--- a/tests/test_api_link.py
+++ b/tests/test_api_link.py
@@ -223,6 +223,74 @@ def test_link_bias_acceleration(
         Jν_js = js.link.bias_acceleration(model=model, data=data, link_index=index)
         assert pytest.approx(Jν_idt) == Jν_js
 
+    # Test that the conversion of the link bias acceleration works as expected.
+    match data.velocity_representation:
+
+        # We exclude the mixed representation because converting the acceleration is
+        # more complex than using the plain 6D transform matrix.
+        case VelRepr.Mixed:
+            pass
+
+        # Inertial-fixed to body-fixed conversion.
+        case VelRepr.Inertial:
+
+            W_H_L = js.model.forward_kinematics(model=model, data=data)
+
+            W_a_bias_WL = jax.vmap(
+                lambda index: js.link.bias_acceleration(
+                    model=model, data=data, link_index=index
+                )
+            )(jnp.arange(model.number_of_links()))
+
+            with data.switch_velocity_representation(VelRepr.Body):
+
+                W_X_L = jax.vmap(
+                    lambda W_H_L: jaxsim.math.Adjoint.from_transform(transform=W_H_L)
+                )(W_H_L)
+
+                L_a_bias_WL = jax.vmap(
+                    lambda index: js.link.bias_acceleration(
+                        model=model, data=data, link_index=index
+                    )
+                )(jnp.arange(model.number_of_links()))
+
+                W_a_bias_WL_converted = jax.vmap(
+                    lambda W_X_L, L_a_bias_WL: W_X_L @ L_a_bias_WL
+                )(W_X_L, L_a_bias_WL)
+
+            assert W_a_bias_WL == pytest.approx(W_a_bias_WL_converted)
+
+        # Body-fixed to inertial-fixed conversion.
+        case VelRepr.Body:
+
+            W_H_L = js.model.forward_kinematics(model=model, data=data)
+
+            L_a_bias_WL = jax.vmap(
+                lambda index: js.link.bias_acceleration(
+                    model=model, data=data, link_index=index
+                )
+            )(jnp.arange(model.number_of_links()))
+
+            with data.switch_velocity_representation(VelRepr.Inertial):
+
+                L_X_W = jax.vmap(
+                    lambda W_H_L: jaxsim.math.Adjoint.from_transform(
+                        transform=W_H_L, inverse=True
+                    )
+                )(W_H_L)
+
+                W_a_bias_WL = jax.vmap(
+                    lambda index: js.link.bias_acceleration(
+                        model=model, data=data, link_index=index
+                    )
+                )(jnp.arange(model.number_of_links()))
+
+                L_a_bias_WL_converted = jax.vmap(
+                    lambda L_X_W, W_a_bias_WL: L_X_W @ W_a_bias_WL
+                )(L_X_W, W_a_bias_WL)
+
+            assert L_a_bias_WL == pytest.approx(L_a_bias_WL_converted)
+
 
 def test_link_jacobian_derivative(
     jaxsim_models_types: js.model.JaxSimModel,