diff --git a/src/plugins/import/ImportXml.py b/src/plugins/import/ImportXml.py
index 6e4b81975..8c9565532 100644
--- a/src/plugins/import/ImportXml.py
+++ b/src/plugins/import/ImportXml.py
@@ -1554,7 +1554,7 @@ class GrampsParser(UpdateCallback):
     def start_surname(self, attrs):
         self.surname = gen.lib.Surname()
         self.surname.set_prefix(attrs.get("prefix", ""))
-        self.surname.set_primary(bool(attrs.get("prim", 1)))
+        self.surname.set_primary(attrs.get("prim", "1") == "1")
         self.surname.set_connector(attrs.get("connector", ""))
         origin_type = attrs.get("derivation", "")
         self.surname.origintype.set_from_xml_str(origin_type)
@@ -2621,8 +2621,11 @@ class GrampsParser(UpdateCallback):
             self.surname = None
 
     def stop_surname(self, tag):
+        """Add surname to name, validating only one primary."""
         if self.name:
             self.surname.set_surname(tag)
+            if any(sname.get_primary() for sname in self.name.get_surname_list()):
+                self.surname.set_primary(False)
             self.name.add_surname(self.surname)
         self.surname = None