diff --git a/API.md b/API.md
index f8f581c3..5c7630a7 100644
--- a/API.md
+++ b/API.md
@@ -25206,6 +25206,7 @@ const logMonitoringProps: LogMonitoringProps = { ... }
 | <code><a href="#cdk-monitoring-constructs.LogMonitoringProps.property.addToSummaryDashboard">addToSummaryDashboard</a></code> | <code>boolean</code> | Flag indicating if the widgets should be added to summary dashboard. |
 | <code><a href="#cdk-monitoring-constructs.LogMonitoringProps.property.useCreatedAlarms">useCreatedAlarms</a></code> | <code><a href="#cdk-monitoring-constructs.IAlarmConsumer">IAlarmConsumer</a></code> | Calls provided function to process all alarms created. |
 | <code><a href="#cdk-monitoring-constructs.LogMonitoringProps.property.logGroupName">logGroupName</a></code> | <code>string</code> | Name of the log group to monitor. |
+| <code><a href="#cdk-monitoring-constructs.LogMonitoringProps.property.addMaxIncomingLogsAlarm">addMaxIncomingLogsAlarm</a></code> | <code>{[ key: string ]: <a href="#cdk-monitoring-constructs.MaxUsageCountThreshold">MaxUsageCountThreshold</a>}</code> | *No description.* |
 | <code><a href="#cdk-monitoring-constructs.LogMonitoringProps.property.addMinIncomingLogsAlarm">addMinIncomingLogsAlarm</a></code> | <code>{[ key: string ]: <a href="#cdk-monitoring-constructs.MinUsageCountThreshold">MinUsageCountThreshold</a>}</code> | *No description.* |
 | <code><a href="#cdk-monitoring-constructs.LogMonitoringProps.property.limit">limit</a></code> | <code>number</code> | Maximum number of log messages to search for. |
 | <code><a href="#cdk-monitoring-constructs.LogMonitoringProps.property.pattern">pattern</a></code> | <code>string</code> | Pattern to search for, e.g. "ERROR". |
@@ -25323,6 +25324,16 @@ Name of the log group to monitor.
 
 ---
 
+##### `addMaxIncomingLogsAlarm`<sup>Optional</sup> <a name="addMaxIncomingLogsAlarm" id="cdk-monitoring-constructs.LogMonitoringProps.property.addMaxIncomingLogsAlarm"></a>
+
+```typescript
+public readonly addMaxIncomingLogsAlarm: {[ key: string ]: MaxUsageCountThreshold};
+```
+
+- *Type:* {[ key: string ]: <a href="#cdk-monitoring-constructs.MaxUsageCountThreshold">MaxUsageCountThreshold</a>}
+
+---
+
 ##### `addMinIncomingLogsAlarm`<sup>Optional</sup> <a name="addMinIncomingLogsAlarm" id="cdk-monitoring-constructs.LogMonitoringProps.property.addMinIncomingLogsAlarm"></a>
 
 ```typescript
diff --git a/lib/monitoring/aws-cloudwatch/LogMonitoring.ts b/lib/monitoring/aws-cloudwatch/LogMonitoring.ts
index 9f9c679c..e37b1ffc 100644
--- a/lib/monitoring/aws-cloudwatch/LogMonitoring.ts
+++ b/lib/monitoring/aws-cloudwatch/LogMonitoring.ts
@@ -17,6 +17,7 @@ import {
   DefaultLogWidgetHeight,
   DefaultSummaryWidgetHeight,
   FullWidth,
+  MaxUsageCountThreshold,
   MetricWithAlarmSupport,
   MinUsageCountThreshold,
   Monitoring,
@@ -55,6 +56,7 @@ export interface LogMonitoringProps
   readonly limit?: number;
 
   readonly addMinIncomingLogsAlarm?: Record<string, MinUsageCountThreshold>;
+  readonly addMaxIncomingLogsAlarm?: Record<string, MaxUsageCountThreshold>;
 }
 
 /**
@@ -116,6 +118,17 @@ export class LogMonitoring extends Monitoring {
       this.addAlarm(createdAlarm);
     }
 
+    for (const disambiguator in props.addMaxIncomingLogsAlarm) {
+      const alarmProps = props.addMaxIncomingLogsAlarm[disambiguator];
+      const createdAlarm = this.usageAlarmFactory.addMaxCountAlarm(
+        this.incomingLogEventsMetric,
+        alarmProps,
+        disambiguator
+      );
+      this.usageAnnotations.push(createdAlarm.annotation);
+      this.addAlarm(createdAlarm);
+    }
+
     props.useCreatedAlarms?.consume(this.createdAlarms());
   }
 
diff --git a/test/monitoring/aws-cloudwatch/LogMonitoring.test.ts b/test/monitoring/aws-cloudwatch/LogMonitoring.test.ts
index 309d8a12..e474656e 100644
--- a/test/monitoring/aws-cloudwatch/LogMonitoring.test.ts
+++ b/test/monitoring/aws-cloudwatch/LogMonitoring.test.ts
@@ -65,6 +65,11 @@ test("snapshot test: with alarms", () => {
         treatMissingDataOverride: TreatMissingData.BREACHING,
       },
     },
+    addMaxIncomingLogsAlarm: {
+      Critical: {
+        maxCount: 9001,
+      },
+    },
     useCreatedAlarms: {
       consume(alarms) {
         numAlarmsCreated = alarms.length;
@@ -73,6 +78,6 @@ test("snapshot test: with alarms", () => {
   });
 
   addMonitoringDashboardsToStack(stack, monitoring);
-  expect(numAlarmsCreated).toStrictEqual(1);
+  expect(numAlarmsCreated).toStrictEqual(2);
   expect(Template.fromStack(stack)).toMatchSnapshot();
 });
diff --git a/test/monitoring/aws-cloudwatch/__snapshots__/LogMonitoring.test.ts.snap b/test/monitoring/aws-cloudwatch/__snapshots__/LogMonitoring.test.ts.snap
index ee793f33..79130ea8 100644
--- a/test/monitoring/aws-cloudwatch/__snapshots__/LogMonitoring.test.ts.snap
+++ b/test/monitoring/aws-cloudwatch/__snapshots__/LogMonitoring.test.ts.snap
@@ -278,6 +278,17 @@ Object {
                   "Arn",
                 ],
               },
+              "\\"]},\\"yAxis\\":{}}},{\\"type\\":\\"metric\\",\\"width\\":6,\\"height\\":4,\\"x\\":6,\\"y\\":0,\\"properties\\":{\\"view\\":\\"timeSeries\\",\\"region\\":\\"",
+              Object {
+                "Ref": "AWS::Region",
+              },
+              "\\",\\"annotations\\":{\\"alarms\\":[\\"",
+              Object {
+                "Fn::GetAtt": Array [
+                  "ScopeTestDummyLogGroupMaxUsageCountCriticalD4E65812",
+                  "Arn",
+                ],
+              },
               "\\"]},\\"yAxis\\":{}}}]}",
             ],
           ],
@@ -299,13 +310,47 @@ Object {
               Object {
                 "Ref": "AWS::Region",
               },
-              "\\",\\"metrics\\":[[\\"AWS/Logs\\",\\"IncomingLogEvents\\",\\"LogGroupName\\",\\"DummyLogGroup\\",{\\"label\\":\\"Logs\\",\\"stat\\":\\"SampleCount\\"}]],\\"annotations\\":{\\"horizontal\\":[{\\"label\\":\\"Logs < 20 for 3 datapoints within 15 minutes\\",\\"value\\":20,\\"yAxis\\":\\"left\\"}]},\\"yAxis\\":{\\"left\\":{\\"min\\":0,\\"label\\":\\"Count\\",\\"showUnits\\":false}}}}]}",
+              "\\",\\"metrics\\":[[\\"AWS/Logs\\",\\"IncomingLogEvents\\",\\"LogGroupName\\",\\"DummyLogGroup\\",{\\"label\\":\\"Logs\\",\\"stat\\":\\"SampleCount\\"}]],\\"annotations\\":{\\"horizontal\\":[{\\"label\\":\\"Logs < 20 for 3 datapoints within 15 minutes\\",\\"value\\":20,\\"yAxis\\":\\"left\\"},{\\"label\\":\\"Logs > 9001 for 3 datapoints within 15 minutes\\",\\"value\\":9001,\\"yAxis\\":\\"left\\"}]},\\"yAxis\\":{\\"left\\":{\\"min\\":0,\\"label\\":\\"Count\\",\\"showUnits\\":false}}}}]}",
             ],
           ],
         },
       },
       "Type": "AWS::CloudWatch::Dashboard",
     },
+    "ScopeTestDummyLogGroupMaxUsageCountCriticalD4E65812": Object {
+      "Properties": Object {
+        "ActionsEnabled": true,
+        "AlarmDescription": "The count is too high.",
+        "AlarmName": "Test-DummyLogGroup-Max-Usage-Count-Critical",
+        "ComparisonOperator": "GreaterThanThreshold",
+        "DatapointsToAlarm": 3,
+        "EvaluationPeriods": 3,
+        "Metrics": Array [
+          Object {
+            "Id": "m1",
+            "Label": "Logs",
+            "MetricStat": Object {
+              "Metric": Object {
+                "Dimensions": Array [
+                  Object {
+                    "Name": "LogGroupName",
+                    "Value": "DummyLogGroup",
+                  },
+                ],
+                "MetricName": "IncomingLogEvents",
+                "Namespace": "AWS/Logs",
+              },
+              "Period": 300,
+              "Stat": "SampleCount",
+            },
+            "ReturnData": true,
+          },
+        ],
+        "Threshold": 9001,
+        "TreatMissingData": "missing",
+      },
+      "Type": "AWS::CloudWatch::Alarm",
+    },
     "ScopeTestDummyLogGroupUsageCountWarningAE5FF03C": Object {
       "Properties": Object {
         "ActionsEnabled": true,
@@ -350,7 +395,7 @@ Object {
               Object {
                 "Ref": "AWS::Region",
               },
-              "\\",\\"metrics\\":[[\\"AWS/Logs\\",\\"IncomingLogEvents\\",\\"LogGroupName\\",\\"DummyLogGroup\\",{\\"label\\":\\"Logs\\",\\"stat\\":\\"SampleCount\\"}]],\\"annotations\\":{\\"horizontal\\":[{\\"label\\":\\"Logs < 20 for 3 datapoints within 15 minutes\\",\\"value\\":20,\\"yAxis\\":\\"left\\"}]},\\"yAxis\\":{\\"left\\":{\\"min\\":0,\\"label\\":\\"Count\\",\\"showUnits\\":false}}}}]}",
+              "\\",\\"metrics\\":[[\\"AWS/Logs\\",\\"IncomingLogEvents\\",\\"LogGroupName\\",\\"DummyLogGroup\\",{\\"label\\":\\"Logs\\",\\"stat\\":\\"SampleCount\\"}]],\\"annotations\\":{\\"horizontal\\":[{\\"label\\":\\"Logs < 20 for 3 datapoints within 15 minutes\\",\\"value\\":20,\\"yAxis\\":\\"left\\"},{\\"label\\":\\"Logs > 9001 for 3 datapoints within 15 minutes\\",\\"value\\":9001,\\"yAxis\\":\\"left\\"}]},\\"yAxis\\":{\\"left\\":{\\"min\\":0,\\"label\\":\\"Count\\",\\"showUnits\\":false}}}}]}",
             ],
           ],
         },