diff --git a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportStartDataFrameAnalyticsAction.java b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportStartDataFrameAnalyticsAction.java
index c0d8d6fbc3260..e30c4e593a7f1 100644
--- a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportStartDataFrameAnalyticsAction.java
+++ b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportStartDataFrameAnalyticsAction.java
@@ -458,7 +458,12 @@ protected void onCancelled() {
 
         @Override
         public void markAsCompleted() {
-            persistProgress(() -> super.markAsCompleted());
+            // It is possible that the stop API has been called in the meantime and that
+            // may also cause this method to be called. We check whether we have already
+            // been marked completed to avoid doing it twice.
+            if (isCompleted() == false) {
+                persistProgress(() -> super.markAsCompleted());
+            }
         }
 
         @Override
diff --git a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/dataframe/DataFrameAnalyticsManager.java b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/dataframe/DataFrameAnalyticsManager.java
index 7856edf2a32ef..b5d288cd11e46 100644
--- a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/dataframe/DataFrameAnalyticsManager.java
+++ b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/dataframe/DataFrameAnalyticsManager.java
@@ -7,6 +7,7 @@
 
 import org.apache.logging.log4j.LogManager;
 import org.apache.logging.log4j.Logger;
+import org.elasticsearch.ResourceNotFoundException;
 import org.elasticsearch.action.ActionListener;
 import org.elasticsearch.action.admin.indices.create.CreateIndexResponse;
 import org.elasticsearch.action.admin.indices.delete.DeleteIndexAction;
@@ -79,7 +80,13 @@ public void execute(DataFrameAnalyticsTask task, DataFrameAnalyticsState current
                     case STARTED:
                         task.updatePersistentTaskState(reindexingState, ActionListener.wrap(
                             updatedTask -> reindexingStateListener.onResponse(config),
-                            reindexingStateListener::onFailure));
+                            error -> {
+                                if (error instanceof ResourceNotFoundException) {
+                                    // The task has been stopped
+                                } else {
+                                    reindexingStateListener.onFailure(error);
+                                }
+                            }));
                         break;
                     // The task has fully reindexed the documents and we should continue on with our analyses
                     case ANALYZING:
@@ -222,7 +229,13 @@ private void startAnalytics(DataFrameAnalyticsTask task, DataFrameAnalyticsConfi
                                 task.markAsCompleted();
                             }
                         }),
-                    error -> task.updateState(DataFrameAnalyticsState.FAILED, error.getMessage())
+                    error -> {
+                        if (error instanceof ResourceNotFoundException) {
+                            // Task has stopped
+                        } else {
+                            task.updateState(DataFrameAnalyticsState.FAILED, error.getMessage());
+                        }
+                    }
                 ));
             },
             error -> task.updateState(DataFrameAnalyticsState.FAILED, error.getMessage())