diff --git a/swh/deposit/api/checks.py b/swh/deposit/api/checks.py
--- a/swh/deposit/api/checks.py
+++ b/swh/deposit/api/checks.py
@@ -13,14 +13,19 @@
 
 from typing import Dict, Optional, Tuple
 
+import iso8601
+
+from swh.deposit.utils import normalize_date
+
 MANDATORY_FIELDS_MISSING = "Mandatory fields are missing"
+INVALID_DATE_FORMAT = "Invalid date format"
 
 
 def check_metadata(metadata: Dict) -> Tuple[bool, Optional[Dict]]:
-    """Check metadata for mandatory field presence.
+    """Check metadata for mandatory field presence and date format.
 
     Args:
-        metadata: Metadata dictionary to check for mandatory fields
+        metadata: Metadata dictionary to check
 
     Returns:
         tuple (status, error_detail): True, None if metadata are
@@ -41,7 +46,29 @@
 
     mandatory_result = [" or ".join(k) for k, v in alternate_fields.items() if not v]
 
-    if mandatory_result == []:
-        return True, None
-    detail = [{"summary": MANDATORY_FIELDS_MISSING, "fields": mandatory_result}]
-    return False, {"metadata": detail}
+    if mandatory_result:
+        detail = [{"summary": MANDATORY_FIELDS_MISSING, "fields": mandatory_result}]
+        return False, {"metadata": detail}
+
+    fields = []
+
+    commit_date = metadata.get("codemeta:datePublished")
+    author_date = metadata.get("codemeta:dateCreated")
+
+    if commit_date:
+        try:
+            normalize_date(commit_date)
+        except iso8601.iso8601.ParseError:
+            fields.append("codemeta:datePublished")
+
+    if author_date:
+        try:
+            normalize_date(author_date)
+        except iso8601.iso8601.ParseError:
+            fields.append("codemeta:dateCreated")
+
+    if fields:
+        detail = [{"summary": INVALID_DATE_FORMAT, "fields": fields}]
+        return False, {"metadata": detail}
+
+    return True, None
diff --git a/swh/deposit/tests/api/test_checks.py b/swh/deposit/tests/api/test_checks.py
--- a/swh/deposit/tests/api/test_checks.py
+++ b/swh/deposit/tests/api/test_checks.py
@@ -24,6 +24,14 @@
             "atom:author": "no one",
         },
         {"atom:url": "some url", "codemeta:name": "bar", "codemeta:author": "no one",},
+        {
+            "atom:url": "some url",
+            "atom:external_identifier": "some id",
+            "atom:title": "bar",
+            "atom:author": "no one",
+            "codemeta:datePublished": "2020-12-21",
+            "codemeta:dateCreated": "2020-12-21",
+        },
     ],
 )
 def test_api_checks_check_metadata_ok(metadata_ok, swh_checks_deposit):
@@ -93,14 +101,25 @@
                 "fields": ["atom:author or codemeta:author"],
             },
         ),
+        (
+            {
+                "atom:url": "some url",
+                "atom:external_identifier": "some id",
+                "atom:title": "bar",
+                "atom:author": "no one",
+                "codemeta:datePublished": "2020-aa-21",
+                "codemeta:dateCreated": "2020-12-bb",
+            },
+            {
+                "summary": "Invalid date format",
+                "fields": ["codemeta:datePublished", "codemeta:dateCreated"],
+            },
+        ),
     ],
 )
 def test_api_checks_check_metadata_ko(
     metadata_ko, expected_summary, swh_checks_deposit
 ):
-    """Missing optional field should be caught
-
-    """
     actual_check, error_detail = check_metadata(metadata_ko)
     assert actual_check is False
     assert error_detail == {"metadata": [expected_summary]}