diff --git a/doc/whatsnew.rst b/doc/whatsnew.rst
index 02ade391..141ed501 100644
--- a/doc/whatsnew.rst
+++ b/doc/whatsnew.rst
@@ -21,6 +21,7 @@ Bug fixes/enhancements:
 - make sure variable ``spercent`` is always defined in ``params_html_table`` functions (reported by @MySlientWind; Issue #768, PR #770)
 - always initialize the variables ``success`` and ``covar`` the ``MinimizerResult`` (reported by Marc W. Pound; PR #771)
 - build package following PEP517/PEP518; use ``pyproject.toml`` and ``setup.cfg``; leave ``setup.py`` for now (PR #777)
+- components used to create a ``CompositeModel`` can now have different independent variables (@Julian-Hochhaus; Discussion #787; PR #788))
 
 
 Deprecations:
diff --git a/lmfit/model.py b/lmfit/model.py
index 5df5b0f1..81acdd93 100644
--- a/lmfit/model.py
+++ b/lmfit/model.py
@@ -1094,7 +1094,7 @@ def __init__(self, left, right, op, **kws):
 
         Notes
         -----
-        The two models must use the same independent variable.
+        The two models can use different independent variables.
 
         """
         if not isinstance(left, Model):
@@ -1116,9 +1116,11 @@ def __init__(self, left, right, op, **kws):
                         "use distinct names.")
             raise NameError(msg)
 
-        # we assume that all the sub-models have the same independent vars
+        # the unique ``independent_vars`` of the left and right model are
+        # combined to ``independent_vars`` of the ``CompositeModel``
         if 'independent_vars' not in kws:
-            kws['independent_vars'] = self.left.independent_vars
+            ivars = self.left.independent_vars + self.right.independent_vars
+            kws['independent_vars'] = list(np.unique(ivars))
         if 'nan_policy' not in kws:
             kws['nan_policy'] = self.left.nan_policy
 
diff --git a/tests/test_model.py b/tests/test_model.py
index ffafef26..1bb227b8 100644
--- a/tests/test_model.py
+++ b/tests/test_model.py
@@ -1247,6 +1247,21 @@ def test_wrapped_model_func(self):
         self.assertTrue(abs(result.params['a'].value - 2.0) < 0.05)
         self.assertTrue(abs(result.params['b'].value - 3.0) < 0.41)
 
+    def test_different_independent_vars_composite_modeld(self):
+        """Regression test for different independent variables in CompositeModel.
+
+        See: https://github.com/lmfit/lmfit-py/discussions/787
+
+        """
+        def two_independent_vars(y, z, a):
+            return a * y + z
+
+        BackgroundModel = Model(two_independent_vars,
+                                independent_vars=["y", "z"], prefix="yz_")
+        PeakModel = Model(gaussian, independent_vars=["x"], prefix="x_")
+        CompModel = BackgroundModel + PeakModel
+        assert CompModel.independent_vars == ['x', 'y', 'z']
+
 
 class TestLinear(CommonTests, unittest.TestCase):