diff --git a/package/CHANGELOG b/package/CHANGELOG
index 5d8328f331..9fe6e8713c 100644
--- a/package/CHANGELOG
+++ b/package/CHANGELOG
@@ -33,6 +33,7 @@ Enhancements
  * Enable parallelization for analysis.nucleicacids.NucPairDist (Issue #4670)
  * Add check and warning for empty (all zero) coordinates in RDKit converter (PR #4824)
  * Added `precision` for XYZWriter (Issue #4775, PR #4771)
+ * explicitly mark `analysis.rdf.InterRDF` and `analysis.rdf.InterRDF` as not parallelizable (Issue #4675)
 
 
 Changes
diff --git a/package/MDAnalysis/analysis/rdf.py b/package/MDAnalysis/analysis/rdf.py
index 02ac014d47..9990a1e2b0 100644
--- a/package/MDAnalysis/analysis/rdf.py
+++ b/package/MDAnalysis/analysis/rdf.py
@@ -218,6 +218,12 @@ class InterRDF(AnalysisBase):
        :class:`~MDAnalysis.analysis.AnalysisBase`.
     """
 
+    @classmethod
+    def get_supported_backends(cls):
+        return ('serial',)
+
+    _analysis_algorithm_is_parallelizable = False
+
     def __init__(
         self,
         g1,
@@ -563,6 +569,12 @@ class InterRDF_s(AnalysisBase):
        The `universe` parameter is superflous.
     """
 
+    @classmethod
+    def get_supported_backends(cls):
+        return ('serial',)
+
+    _analysis_algorithm_is_parallelizable = False
+    
     def __init__(
         self,
         u,
diff --git a/testsuite/MDAnalysisTests/analysis/test_rdf.py b/testsuite/MDAnalysisTests/analysis/test_rdf.py
index d3507e5673..4a8fe46994 100644
--- a/testsuite/MDAnalysisTests/analysis/test_rdf.py
+++ b/testsuite/MDAnalysisTests/analysis/test_rdf.py
@@ -152,3 +152,21 @@ def test_unknown_norm(sels):
     s1, s2 = sels
     with pytest.raises(ValueError, match="invalid norm"):
         InterRDF(s1, s2, sels, norm="foo")
+
+@pytest.mark.parametrize(
+    "classname,is_parallelizable",
+    [
+        (mda.analysis.rdf, False),
+    ]
+)
+def test_class_is_parallelizable(classname, is_parallelizable):
+    assert classname.InterRDF._analysis_algorithm_is_parallelizable == is_parallelizable
+
+@pytest.mark.parametrize(
+    "classname,backends",
+    [
+        (mda.analysis.rdf,  ('serial',)),
+    ]
+)
+def test_supported_backends(classname, backends):
+    assert classname.InterRDF.get_supported_backends() == backends
diff --git a/testsuite/MDAnalysisTests/analysis/test_rdf_s.py b/testsuite/MDAnalysisTests/analysis/test_rdf_s.py
index 5c6e8b6031..bdce3eed64 100644
--- a/testsuite/MDAnalysisTests/analysis/test_rdf_s.py
+++ b/testsuite/MDAnalysisTests/analysis/test_rdf_s.py
@@ -171,3 +171,21 @@ def test_rdf_attr_warning(rdf, attr):
     wmsg = f"The `{attr}` attribute was deprecated in MDAnalysis 2.0.0"
     with pytest.warns(DeprecationWarning, match=wmsg):
         getattr(rdf, attr) is rdf.results[attr]
+
+@pytest.mark.parametrize(
+    "classname,is_parallelizable",
+    [
+        (mda.analysis.rdf, False),
+    ]
+)
+def test_class_is_parallelizable(classname, is_parallelizable):
+    assert classname.InterRDF_s._analysis_algorithm_is_parallelizable == is_parallelizable
+
+@pytest.mark.parametrize(
+    "classname,backends",
+    [
+        (mda.analysis.rdf,  ('serial',)),
+    ]
+)
+def test_supported_backends(classname, backends):
+    assert classname.InterRDF_s.get_supported_backends() == backends