diff --git a/swh/deposit/parsers.py b/swh/deposit/parsers.py
--- a/swh/deposit/parsers.py
+++ b/swh/deposit/parsers.py
@@ -8,6 +8,7 @@
 
 """
 
+import logging
 from typing import Dict, Optional, Union
 from xml.parsers.expat import ExpatError
 
@@ -26,6 +27,8 @@
     parse_swhid,
 )
 
+logger = logging.getLogger(__name__)
+
 
 class SWHFileUploadZipParser(FileUploadParser):
     """File upload parser limited to zip archive.
@@ -142,6 +145,9 @@
         Either swhid or origin reference if any. None otherwise.
 
     """  # noqa
+    visit_swhid = None
+    anchor_swhid = None
+
     swh_deposit = metadata.get("swh:deposit")
     if not swh_deposit:
         return None
@@ -184,4 +190,18 @@
                     f"visit qualifier should be a core SWHID with type {SNAPSHOT}"
                 )
 
+        if (
+            visit_swhid
+            and anchor_swhid
+            and visit_swhid.object_type == SNAPSHOT
+            and anchor_swhid.object_type == SNAPSHOT
+        ):
+            logger.warn(
+                "SWHID use of both anchor and visit targeting "
+                f"a snapshot: {swhid_reference}"
+            )
+            raise ValidationError(
+                "'anchor=swh:1:snp:' is not supported when 'visit' is also provided."
+            )
+
     return swhid_reference
diff --git a/swh/deposit/tests/api/test_parsers.py b/swh/deposit/tests/api/test_parsers.py
--- a/swh/deposit/tests/api/test_parsers.py
+++ b/swh/deposit/tests/api/test_parsers.py
@@ -224,7 +224,11 @@
         (
             "swh:1:rev:c4993c872593e960dc84e4430dbbfbc34fd706d0;anchor=swh:1:cnt:b5f505b005435fa5c4fa4c279792bd7b17167c04;path=/",  # noqa
             "anchor qualifier should be a core SWHID with type one of",
-        ),  # noqa
+        ),
+        (
+            "swh:1:rev:c4993c872593e960dc84e4430dbbfbc34fd706d0;visit=swh:1:snp:0175049fc45055a3824a1675ac06e3711619a55a;anchor=swh:1:snp:b5f505b005435fa5c4fa4c279792bd7b17167c04",  # noqa
+            "anchor=swh:1:snp",
+        ),
     ],
 )
 def test_parse_swh_reference_invalid_swhid(invalid_swhid, error_msg, xml_with_swhid):