diff --git a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportCloseJobAction.java b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportCloseJobAction.java
index 63b8f90a114d0..4f9fb89509cb7 100644
--- a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportCloseJobAction.java
+++ b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportCloseJobAction.java
@@ -6,6 +6,7 @@
 package org.elasticsearch.xpack.ml.action;
 
 import org.elasticsearch.ElasticsearchException;
+import org.elasticsearch.ResourceNotFoundException;
 import org.elasticsearch.action.ActionListener;
 import org.elasticsearch.action.ActionListenerResponseHandler;
 import org.elasticsearch.action.FailedNodeException;
@@ -17,6 +18,7 @@
 import org.elasticsearch.cluster.metadata.IndexNameExpressionResolver;
 import org.elasticsearch.cluster.node.DiscoveryNodes;
 import org.elasticsearch.cluster.service.ClusterService;
+import org.elasticsearch.common.Strings;
 import org.elasticsearch.common.inject.Inject;
 import org.elasticsearch.common.io.stream.StreamInput;
 import org.elasticsearch.common.settings.Settings;
@@ -291,7 +293,12 @@ protected void taskOperation(CloseJobAction.Request request, TransportOpenJobAct
             threadPool.executor(MachineLearning.UTILITY_THREAD_POOL_NAME).execute(new AbstractRunnable() {
                 @Override
                 public void onFailure(Exception e) {
-                    listener.onFailure(e);
+                    if (e instanceof ResourceNotFoundException && Strings.isAllOrWildcard(new String[]{request.getJobId()})) {
+                        jobTask.closeJob("close job (api)");
+                        listener.onResponse(new CloseJobAction.Response(true));
+                    } else {
+                        listener.onFailure(e);
+                    }
                 }
 
                 @Override
@@ -356,7 +363,10 @@ public void onResponse(PersistentTasksCustomMetaData.PersistentTask<?> task) {
                             @Override
                             public void onFailure(Exception e) {
                                 final int slot = counter.incrementAndGet();
-                                failures.set(slot - 1, e);
+                                if ((e instanceof ResourceNotFoundException &&
+                                    Strings.isAllOrWildcard(new String[]{request.getJobId()})) == false) {
+                                    failures.set(slot - 1, e);
+                                }
                                 if (slot == numberOfJobs) {
                                     sendResponseOrFailure(request.getJobId(), listener, failures);
                                 }
diff --git a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportStopDatafeedAction.java b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportStopDatafeedAction.java
index 77910f21f67d1..5d9d900aaa8dd 100644
--- a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportStopDatafeedAction.java
+++ b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/action/TransportStopDatafeedAction.java
@@ -17,6 +17,7 @@
 import org.elasticsearch.cluster.metadata.IndexNameExpressionResolver;
 import org.elasticsearch.cluster.node.DiscoveryNodes;
 import org.elasticsearch.cluster.service.ClusterService;
+import org.elasticsearch.common.Strings;
 import org.elasticsearch.common.inject.Inject;
 import org.elasticsearch.common.io.stream.StreamInput;
 import org.elasticsearch.common.settings.Settings;
@@ -193,7 +194,10 @@ public void onResponse(PersistentTasksCustomMetaData.PersistentTask<?> persisten
                     @Override
                     public void onFailure(Exception e) {
                         final int slot = counter.incrementAndGet();
-                        failures.set(slot - 1, e);
+                        if ((e instanceof ResourceNotFoundException &&
+                            Strings.isAllOrWildcard(new String[]{request.getDatafeedId()})) == false) {
+                            failures.set(slot - 1, e);
+                        }
                         if (slot == startedDatafeeds.size()) {
                             sendResponseOrFailure(request.getDatafeedId(), listener, failures);
                         }
@@ -221,7 +225,13 @@ protected void taskOperation(StopDatafeedAction.Request request, TransportStartD
                     threadPool.executor(MachineLearning.UTILITY_THREAD_POOL_NAME).execute(new AbstractRunnable() {
                         @Override
                         public void onFailure(Exception e) {
-                            listener.onFailure(e);
+                            if ((e instanceof ResourceNotFoundException &&
+                                Strings.isAllOrWildcard(new String[]{request.getDatafeedId()}))) {
+                                datafeedTask.stop("stop_datafeed (api)", request.getStopTimeout());
+                                listener.onResponse(new StopDatafeedAction.Response(true));
+                            } else {
+                                listener.onFailure(e);
+                            }
                         }
 
                         @Override