diff --git a/moto/logs/models.py b/moto/logs/models.py
index dcc0e85e1..8425f87f2 100644
--- a/moto/logs/models.py
+++ b/moto/logs/models.py
@@ -485,20 +485,39 @@ class LogsBackend(BaseBackend):
     def describe_log_groups(self, limit, log_group_name_prefix, next_token):
         if log_group_name_prefix is None:
             log_group_name_prefix = ""
-        if next_token is None:
-            next_token = 0
 
         groups = [
             group.to_describe_dict()
             for name, group in self.groups.items()
             if name.startswith(log_group_name_prefix)
         ]
-        groups = sorted(groups, key=lambda x: x["creationTime"], reverse=True)
-        groups_page = groups[next_token : next_token + limit]
+        groups = sorted(groups, key=lambda x: x["logGroupName"])
 
-        next_token += limit
-        if next_token >= len(groups):
-            next_token = None
+        index_start = 0
+        if next_token:
+            try:
+                index_start = (
+                    next(
+                        index
+                        for (index, d) in enumerate(groups)
+                        if d["logGroupName"] == next_token
+                    )
+                    + 1
+                )
+            except StopIteration:
+                index_start = 0
+                # AWS returns an empty list if it receives an invalid token.
+                groups = []
+
+        index_end = index_start + limit
+        if index_end > len(groups):
+            index_end = len(groups)
+
+        groups_page = groups[index_start:index_end]
+
+        next_token = None
+        if groups_page and index_end < len(groups):
+            next_token = groups_page[-1]["logGroupName"]
 
         return groups_page, next_token
 
diff --git a/moto/logs/responses.py b/moto/logs/responses.py
index 9e6886a42..715c4b5c1 100644
--- a/moto/logs/responses.py
+++ b/moto/logs/responses.py
@@ -42,7 +42,10 @@ class LogsResponse(BaseResponse):
         groups, next_token = self.logs_backend.describe_log_groups(
             limit, log_group_name_prefix, next_token
         )
-        return json.dumps({"logGroups": groups, "nextToken": next_token})
+        result = {"logGroups": groups}
+        if next_token:
+            result["nextToken"] = next_token
+        return json.dumps(result)
 
     def create_log_stream(self):
         log_group_name = self._get_param("logGroupName")
diff --git a/tests/test_logs/test_logs.py b/tests/test_logs/test_logs.py
index e234cc561..648d561aa 100644
--- a/tests/test_logs/test_logs.py
+++ b/tests/test_logs/test_logs.py
@@ -458,3 +458,39 @@ def test_describe_subscription_filters_errors():
     ex.response["Error"]["Message"].should.equal(
         "The specified log group does not exist"
     )
+
+
+@mock_logs
+def test_describe_log_groups_paging():
+    client = boto3.client("logs", "us-east-1")
+
+    group_names = [
+        "/aws/lambda/lowercase-dev",
+        "/aws/lambda/FileMonitoring",
+        "/aws/events/GetMetricData",
+        "/aws/lambda/fileAvailable",
+    ]
+
+    for name in group_names:
+        client.create_log_group(logGroupName=name)
+
+    resp = client.describe_log_groups()
+    resp["logGroups"].should.have.length_of(4)
+    resp.should_not.have.key("nextToken")
+
+    resp = client.describe_log_groups(limit=2)
+    resp["logGroups"].should.have.length_of(2)
+    resp["nextToken"].should.equal("/aws/lambda/FileMonitoring")
+
+    resp = client.describe_log_groups(nextToken=resp["nextToken"], limit=1)
+    resp["logGroups"].should.have.length_of(1)
+    resp["nextToken"].should.equal("/aws/lambda/fileAvailable")
+
+    resp = client.describe_log_groups(nextToken=resp["nextToken"])
+    resp["logGroups"].should.have.length_of(1)
+    resp["logGroups"][0]["logGroupName"].should.equal("/aws/lambda/lowercase-dev")
+    resp.should_not.have.key("nextToken")
+
+    resp = client.describe_log_groups(nextToken="invalid-token")
+    resp["logGroups"].should.have.length_of(0)
+    resp.should_not.have.key("nextToken")