diff --git a/jose/jwt.py b/jose/jwt.py
index f47e4dd..e8900a4 100644
--- a/jose/jwt.py
+++ b/jose/jwt.py
@@ -352,8 +352,8 @@ def _validate_aud(claims, audience=None):
     """
 
     if "aud" not in claims:
-        # if audience:
-        #     raise JWTError('Audience claim expected, but not in claims')
+        if audience is not None:
+            raise JWTClaimsError("Token is missing the 'aud' claim")
         return
 
     audience_claims = claims["aud"]
diff --git a/tests/test_jwt.py b/tests/test_jwt.py
index f9d54cd..9244c2d 100644
--- a/tests/test_jwt.py
+++ b/tests/test_jwt.py
@@ -353,11 +353,17 @@ def test_aud_case_sensitive(self, key):
         with pytest.raises(JWTError):
             jwt.decode(token, key, audience="AUDIENCE")
 
-    def test_aud_empty_claim(self, claims, key):
-        aud = "audience"
+    def test_aud_missing_claim_no_audience(self, claims, key):
+        # Token without 'aud' and no audience expected: should pass
+        token = jwt.encode(claims, key)
+        jwt.decode(token, key)
 
+    def test_aud_missing_claim_with_audience(self, claims, key):
+        # Token without 'aud' but caller requires an audience: should be rejected
+        aud = "audience"
         token = jwt.encode(claims, key)
-        jwt.decode(token, key, audience=aud)
+        with pytest.raises(JWTError):
+            jwt.decode(token, key, audience=aud)
 
     def test_aud_not_string_or_list(self, key):
         aud = 1
@@ -522,12 +528,15 @@ def test_require(self, claims, key, claim, value):
         if callable(value):
             value = value()
         options = {"require_" + claim: True, "verify_" + claim: False}
+        # Only pass audience when the claim under test is actually "aud";
+        # passing audience for other claims would wrongly trigger the missing-aud check.
+        audience = str(value) if claim == "aud" else None
 
         token = jwt.encode(claims, key)
         with pytest.raises(JWTError):
-            jwt.decode(token, key, options=options, audience=str(value))
+            jwt.decode(token, key, options=options, audience=audience)
 
         new_claims = dict(claims)
         new_claims[claim] = value
         token = jwt.encode(new_claims, key)
-        jwt.decode(token, key, options=options, audience=str(value))
+        jwt.decode(token, key, options=options, audience=audience)