diff --git a/jedi/inference/gradual/annotation.py b/jedi/inference/gradual/annotation.py
index 957ec660..c2abacfb 100644
--- a/jedi/inference/gradual/annotation.py
+++ b/jedi/inference/gradual/annotation.py
@@ -37,12 +37,15 @@ def infer_annotation(context, annotation):
             "Inferred typing index %s should lead to 1 object, not %s" % (annotation, value_set))
         return value_set
 
-    inferred_value = list(value_set)[0]
-    if is_string(inferred_value):
-        result = _get_forward_reference_node(context, inferred_value.get_safe_value())
-        if result is not None:
-            return context.infer_node(result)
-    return value_set
+    strings_removed = NO_VALUES
+    for part in value_set:
+        if is_string(part):
+            result = _get_forward_reference_node(context, part.get_safe_value())
+            if result is not None:
+                strings_removed |= context.infer_node(result)
+                continue
+        strings_removed |= ValueSet([part])
+    return strings_removed
 
 
 def _infer_annotation_string(context, string, index=None):
diff --git a/test/completion/pep0484_basic.py b/test/completion/pep0484_basic.py
index 35edcb8c..f1d7677e 100644
--- a/test/completion/pep0484_basic.py
+++ b/test/completion/pep0484_basic.py
@@ -230,3 +230,11 @@ def use_type_with_annotation() -> type[int]: ...
 
 #? int
 use_type_with_annotation()
+
+def union_with_forward_references(x: int | "str", y: "int" | str, z: "int | str"):
+    #? int() str()
+    x
+    #? int() str()
+    y
+    #? int() str()
+    z