diff --git a/bilby/core/result.py b/bilby/core/result.py
index f643d919e9483bb3b0e3237d390fdf4a784a988a..d90876dc0f67084fb978426c36bb3a88bac10e72 100644
--- a/bilby/core/result.py
+++ b/bilby/core/result.py
@@ -1295,7 +1295,8 @@ class ResultList(list):
             raise CombineResultError("Cannot combine results: inconsistent parameters")
 
     def _check_consistent_data(self):
-        if not np.all([res.log_noise_evidence == self[0].log_noise_evidence for res in self]):
+        if not np.all([res.log_noise_evidence == self[0].log_noise_evidence for res in self])\
+                and not np.all([np.isnan(res.log_noise_evidence) for res in self]):
             raise CombineResultError("Cannot combine results: inconsistent data")
 
     def _check_consistent_sampler(self):
diff --git a/test/result_test.py b/test/result_test.py
index 049c9d4076e535b18bac2932de558918ab077536..269afaa8e37164f422eca10fd784e272bd596b03 100644
--- a/test/result_test.py
+++ b/test/result_test.py
@@ -508,6 +508,11 @@ class TestResultList(unittest.TestCase):
         with self.assertRaises(bilby.result.CombineResultError):
             self.nested_results.combine()
 
+    def test_combine_inconsistent_data_nan(self):
+        self.nested_results[0].log_noise_evidence = np.nan
+        self.nested_results[1].log_noise_evidence = np.nan
+        self.nested_results.combine()
+
     def test_combine_inconsistent_sampling_data(self):
         result = bilby.core.result.Result(
             label=self.label, outdir=self.outdir, sampler='cpnest',