diff --git a/release-notes/next-release.md b/release-notes/next-release.md
index 287813643..e761c5b2f 100644
--- a/release-notes/next-release.md
+++ b/release-notes/next-release.md
@@ -9,6 +9,7 @@
 of SBO:0000633 (see https://sourceforge.net/p/sbo/term-request/113/)
 * Correct reading and writing of subsystem in mat.
 * General cleanup of code in mat.py
+* Fixed issue 673 (problem when copying reaction from a different model)
 
 ## Other
 
diff --git a/src/cobra/core/model.py b/src/cobra/core/model.py
index a3fe5b588..fe71e5047 100644
--- a/src/cobra/core/model.py
+++ b/src/cobra/core/model.py
@@ -863,13 +863,13 @@ def remove_reactions(
                 reaction._model = None
 
                 for met in reaction.metabolites:
-                    if reaction in met.reactions:
+                    if reaction in met._reaction:
                         met.reaction_remove(reaction, context)
                         if remove_orphans and len(met.reactions) == 0:
                             self.remove_metabolites(met)
 
                 for gene in reaction.genes:
-                    if reaction in gene.reactions:
+                    if reaction in gene._reaction:
                         gene.reaction_remove(reaction, context)
 
                         if remove_orphans and len(gene.reactions) == 0:
diff --git a/src/cobra/core/species.py b/src/cobra/core/species.py
index 3ea9cef63..658b5d55a 100644
--- a/src/cobra/core/species.py
+++ b/src/cobra/core/species.py
@@ -58,13 +58,15 @@ def reactions(self) -> FrozenSet:
             A frozenset that includes the reactions of the species.
         """
         if self.model and self.__class__.__name__ == "Gene":
-            return self.model.reactions.query(lambda x: self in x, "genes")
+            return frozenset(self.model.reactions.query(lambda x: self in x, "genes"))
         elif self.model and self.__class__.__name__ == "Metabolite":
-            return self.model.reactions.query(lambda x: self in x, "metabolites")
+            return frozenset(
+                self.model.reactions.query(lambda x: self in x, "metabolites")
+            )
         return frozenset(self._reaction)
 
     def reaction_add(
-        self, reaction: Reaction, context: Optional[HistoryManager] = None
+        self, reaction: "Reaction", context: Optional[HistoryManager] = None
     ) -> None:
         """Add reaction to .reaction field, with context.
 
@@ -81,7 +83,7 @@ def reaction_add(
             context(partial(self._reaction.remove, reaction))
 
     def reaction_remove(
-        self, reaction: Reaction, context: Optional[HistoryManager] = None
+        self, reaction: "Reaction", context: Optional[HistoryManager] = None
     ) -> None:
         """Remove reaction from .reaction field, with context.