diff --git a/test/e2e/e2e.go b/test/e2e/e2e.go
index 89aa54af59..cc8dfbaf6d 100644
--- a/test/e2e/e2e.go
+++ b/test/e2e/e2e.go
@@ -137,7 +137,11 @@ var _ = ginkgo.SynchronizedBeforeSuite(func() []byte {
 	// test pods from running, and tests that ensure all pods are running and
 	// ready will fail).
 	podStartupTimeout := framework.TestContext.SystemPodsStartupTimeout
-	if err := framework.WaitForPodsRunningReady(c, metav1.NamespaceSystem, int32(framework.TestContext.MinStartupPods), podStartupTimeout, framework.ImagePullerLabels, true); err != nil {
+	// TODO: In large clusters, we often observe a non-starting pods due to
+	// #41007. To avoid those pods preventing the whole test runs (and just
+	// wasting the whole run), we allow for some not-ready pods (with the
+	// number equal to the number of allowed not-ready nodes).
+	if err := framework.WaitForPodsRunningReady(c, metav1.NamespaceSystem, int32(framework.TestContext.MinStartupPods), int32(framework.TestContext.AllowedNotReadyNodes), podStartupTimeout, framework.ImagePullerLabels, true); err != nil {
 		framework.DumpAllNamespaceInfo(c, metav1.NamespaceSystem)
 		framework.LogFailedContainers(c, metav1.NamespaceSystem, framework.Logf)
 		runKubernetesServiceTestContainer(c, metav1.NamespaceDefault)
diff --git a/test/e2e/framework/util.go b/test/e2e/framework/util.go
index dec506c6b7..2fcd1af714 100644
--- a/test/e2e/framework/util.go
+++ b/test/e2e/framework/util.go
@@ -495,8 +495,7 @@ func WaitForPodsSuccess(c clientset.Interface, ns string, successPodLabels map[s
 // and some in Success. This is to allow the client to decide if "Success"
 // means "Ready" or not.
 // If skipSucceeded is true, any pods that are Succeeded are not counted.
-func WaitForPodsRunningReady(c clientset.Interface, ns string, minPods int32, timeout time.Duration, ignoreLabels map[string]string, skipSucceeded bool) error {
-
+func WaitForPodsRunningReady(c clientset.Interface, ns string, minPods, allowedNotReadyPods int32, timeout time.Duration, ignoreLabels map[string]string, skipSucceeded bool) error {
 	ignoreSelector := labels.SelectorFromSet(ignoreLabels)
 	start := time.Now()
 	Logf("Waiting up to %v for all pods (need at least %d) in namespace '%s' to be running and ready",
@@ -504,6 +503,7 @@ func WaitForPodsRunningReady(c clientset.Interface, ns string, minPods int32, ti
 	wg := sync.WaitGroup{}
 	wg.Add(1)
 	var waitForSuccessError error
+	var ignoreNotReady bool
 	badPods := []v1.Pod{}
 	desiredPods := 0
 	go func() {
@@ -544,6 +544,7 @@ func WaitForPodsRunningReady(c clientset.Interface, ns string, minPods int32, ti
 			return false, nil
 		}
 		nOk := int32(0)
+		notReady := int32(0)
 		badPods = []v1.Pod{}
 		desiredPods = len(podList.Items)
 		for _, pod := range podList.Items {
@@ -564,6 +565,7 @@ func WaitForPodsRunningReady(c clientset.Interface, ns string, minPods int32, ti
 				return false, errors.New("unexpected Succeeded pod state")
 			case pod.Status.Phase != v1.PodFailed:
 				Logf("The status of Pod %s is %s (Ready = false), waiting for it to be either Running (with Ready = true) or Failed", pod.ObjectMeta.Name, pod.Status.Phase)
+				notReady++
 				badPods = append(badPods, pod)
 			default:
 				if _, ok := pod.Annotations[v1.CreatedByAnnotation]; !ok {
@@ -581,10 +583,14 @@ func WaitForPodsRunningReady(c clientset.Interface, ns string, minPods int32, ti
 		if replicaOk == replicas && nOk >= minPods && len(badPods) == 0 {
 			return true, nil
 		}
+		ignoreNotReady = (notReady <= allowedNotReadyPods)
 		logPodStates(badPods)
 		return false, nil
 	}) != nil {
-		return errors.New(errorBadPodsStates(badPods, desiredPods, ns, "RUNNING and READY", timeout))
+		if !ignoreNotReady {
+			return errors.New(errorBadPodsStates(badPods, desiredPods, ns, "RUNNING and READY", timeout))
+		}
+		Logf("Number of not-ready pods is allowed.")
 	}
 	wg.Wait()
 	if waitForSuccessError != nil {
diff --git a/test/e2e/mesos.go b/test/e2e/mesos.go
index 09b87d8f19..fc70491fb1 100644
--- a/test/e2e/mesos.go
+++ b/test/e2e/mesos.go
@@ -68,7 +68,7 @@ var _ = framework.KubeDescribe("Mesos", func() {
 		nodelist := framework.GetReadySchedulableNodesOrDie(client)
 		const ns = "static-pods"
 		numpods := int32(len(nodelist.Items))
-		framework.ExpectNoError(framework.WaitForPodsRunningReady(client, ns, numpods, wait.ForeverTestTimeout, map[string]string{}, false),
+		framework.ExpectNoError(framework.WaitForPodsRunningReady(client, ns, numpods, 0, wait.ForeverTestTimeout, map[string]string{}, false),
 			fmt.Sprintf("number of static pods in namespace %s is %d", ns, numpods))
 	})
 
diff --git a/test/e2e/resize_nodes.go b/test/e2e/resize_nodes.go
index 62b43b6442..157ba97c33 100644
--- a/test/e2e/resize_nodes.go
+++ b/test/e2e/resize_nodes.go
@@ -237,7 +237,7 @@ var _ = framework.KubeDescribe("Nodes [Disruptive]", func() {
 			// Many e2e tests assume that the cluster is fully healthy before they start.  Wait until
 			// the cluster is restored to health.
 			By("waiting for system pods to successfully restart")
-			err := framework.WaitForPodsRunningReady(c, metav1.NamespaceSystem, systemPodsNo, framework.PodReadyBeforeTimeout, ignoreLabels, true)
+			err := framework.WaitForPodsRunningReady(c, metav1.NamespaceSystem, systemPodsNo, 0, framework.PodReadyBeforeTimeout, ignoreLabels, true)
 			Expect(err).NotTo(HaveOccurred())
 			By("waiting for image prepulling pods to complete")
 			framework.WaitForPodsSuccess(c, metav1.NamespaceSystem, framework.ImagePullerLabels, imagePrePullingTimeout)
diff --git a/test/e2e/scheduler_predicates.go b/test/e2e/scheduler_predicates.go
index c13b1ae1a4..d0cb036d54 100644
--- a/test/e2e/scheduler_predicates.go
+++ b/test/e2e/scheduler_predicates.go
@@ -90,7 +90,7 @@ var _ = framework.KubeDescribe("SchedulerPredicates [Serial]", func() {
 			}
 		}
 
-		err = framework.WaitForPodsRunningReady(cs, metav1.NamespaceSystem, int32(systemPodsNo), framework.PodReadyBeforeTimeout, ignoreLabels, true)
+		err = framework.WaitForPodsRunningReady(cs, metav1.NamespaceSystem, int32(systemPodsNo), 0, framework.PodReadyBeforeTimeout, ignoreLabels, true)
 		Expect(err).NotTo(HaveOccurred())
 
 		for _, node := range nodeList.Items {