diff --git a/spec/Observable-spec.ts b/spec/Observable-spec.ts
index 7e86b66d01..3627c37f15 100644
--- a/spec/Observable-spec.ts
+++ b/spec/Observable-spec.ts
@@ -901,5 +901,20 @@ describe('Observable.lift', () => {
           ]);
           done();
         });
-    });
+  });
+
+  it('should not swallow internal errors', () => {
+    const consoleStub = sinon.stub(console, 'warn');
+    try {
+      let source = new Observable<number>(observer => observer.next(42));
+      for (let i = 0; i < 10000; ++i) {
+        let base = source;
+        source = new Observable<number>(observer => base.subscribe(observer));
+      }
+      source.subscribe();
+      expect(consoleStub).to.have.property('called', true);
+    } finally {
+      consoleStub.restore();
+    }
+  });
 });
diff --git a/spec/observables/bindCallback-spec.ts b/spec/observables/bindCallback-spec.ts
index bfe915caec..e2caf8866f 100644
--- a/spec/observables/bindCallback-spec.ts
+++ b/spec/observables/bindCallback-spec.ts
@@ -280,4 +280,18 @@ describe('bindCallback', () => {
       expect(calls).to.equal(0);
     });
   });
+
+  it('should not swallow post-callback errors', () => {
+    function badFunction(callback: (answer: number) => void): void {
+      callback(42);
+      throw new Error('kaboom');
+    }
+    const consoleStub = sinon.stub(console, 'warn');
+    try {
+      bindCallback(badFunction)().subscribe();
+      expect(consoleStub).to.have.property('called', true);
+    } finally {
+      consoleStub.restore();
+    }
+  });
 });
diff --git a/spec/observables/bindNodeCallback-spec.ts b/spec/observables/bindNodeCallback-spec.ts
index 19b019b4f2..874385f57e 100644
--- a/spec/observables/bindNodeCallback-spec.ts
+++ b/spec/observables/bindNodeCallback-spec.ts
@@ -278,4 +278,18 @@ describe('bindNodeCallback', () => {
     expect(results1).to.deep.equal([42, 'done']);
     expect(results2).to.deep.equal([42, 'done']);
   });
+
+  it('should not swallow post-callback errors', () => {
+    function badFunction(callback: (error: Error, answer: number) => void): void {
+      callback(null, 42);
+      throw new Error('kaboom');
+    }
+    const consoleStub = sinon.stub(console, 'warn');
+    try {
+      bindNodeCallback(badFunction)().subscribe();
+      expect(consoleStub).to.have.property('called', true);
+    } finally {
+      consoleStub.restore();
+    }
+  });
 });
diff --git a/spec/util/canReportError-spec.ts b/spec/util/canReportError-spec.ts
new file mode 100644
index 0000000000..77df00d2ae
--- /dev/null
+++ b/spec/util/canReportError-spec.ts
@@ -0,0 +1,29 @@
+import { expect } from 'chai';
+import { noop, Subject, Subscriber } from 'rxjs';
+import { canReportError } from 'rxjs/internal/util/canReportError';
+
+describe('canReportError', () => {
+  it('should report errors to an observer if possible', () => {
+    const subscriber = new Subscriber<{}>(noop, noop);
+    expect(canReportError(subscriber)).to.be.true;
+  });
+
+  it('should not report errors to a stopped observer', () => {
+    const subscriber = new Subscriber<{}>(noop, noop);
+    subscriber.error(new Error('kaboom'));
+    expect(canReportError(subscriber)).to.be.false;
+  });
+
+  it('should not report errors to a closed subject', () => {
+    const subject = new Subject<{}>();
+    subject.unsubscribe();
+    expect(canReportError(subject)).to.be.false;
+  });
+
+  it('should not report errors an observer with a stopped destination', () => {
+    const destination = new Subscriber<{}>(noop, noop);
+    const subscriber = new Subscriber<{}>(destination);
+    destination.error(new Error('kaboom'));
+    expect(canReportError(subscriber)).to.be.false;
+  });
+});
diff --git a/src/internal/Observable.ts b/src/internal/Observable.ts
index d9e8f0c0d5..78b7506190 100644
--- a/src/internal/Observable.ts
+++ b/src/internal/Observable.ts
@@ -2,6 +2,7 @@ import { Operator } from './Operator';
 import { Subscriber } from './Subscriber';
 import { Subscription } from './Subscription';
 import { TeardownLogic, OperatorFunction, PartialObserver, Subscribable } from './types';
+import { canReportError } from './util/canReportError';
 import { toSubscriber } from './util/toSubscriber';
 import { iif } from './observable/iif';
 import { throwError } from './observable/throwError';
@@ -226,7 +227,11 @@ export class Observable<T> implements Subscribable<T> {
         sink.syncErrorThrown = true;
         sink.syncErrorValue = err;
       }
-      sink.error(err);
+      if (canReportError(sink)) {
+        sink.error(err);
+      } else {
+        console.warn(err);
+      }
     }
   }
 
diff --git a/src/internal/Subscriber.ts b/src/internal/Subscriber.ts
index d7dd3c84de..7f81c5814b 100644
--- a/src/internal/Subscriber.ts
+++ b/src/internal/Subscriber.ts
@@ -325,6 +325,6 @@ export class SafeSubscriber<T> extends Subscriber<T> {
   }
 }
 
-function isTrustedSubscriber(obj: any) {
+export function isTrustedSubscriber(obj: any) {
   return obj instanceof Subscriber || ('_addParentTeardownLogic' in obj && obj[rxSubscriberSymbol]);
 }
diff --git a/src/internal/observable/bindCallback.ts b/src/internal/observable/bindCallback.ts
index 1ec55260ad..3166a41fa2 100644
--- a/src/internal/observable/bindCallback.ts
+++ b/src/internal/observable/bindCallback.ts
@@ -3,6 +3,7 @@ import { Observable } from '../Observable';
 import { AsyncSubject } from '../AsyncSubject';
 import { Subscriber } from '../Subscriber';
 import { map } from '../operators/map';
+import { canReportError } from '../util/canReportError';
 import { isArray } from '../util/isArray';
 import { isScheduler } from '../util/isScheduler';
 
@@ -204,7 +205,11 @@ export function bindCallback<T>(
           try {
             callbackFunc.apply(context, [...args, handler]);
           } catch (err) {
-            subject.error(err);
+            if (canReportError(subject)) {
+              subject.error(err);
+            } else {
+              console.warn(err);
+            }
           }
         }
         return subject.subscribe(subscriber);
diff --git a/src/internal/observable/bindNodeCallback.ts b/src/internal/observable/bindNodeCallback.ts
index 4aefc2f755..d40e4fb6a4 100644
--- a/src/internal/observable/bindNodeCallback.ts
+++ b/src/internal/observable/bindNodeCallback.ts
@@ -3,6 +3,7 @@ import { AsyncSubject } from '../AsyncSubject';
 import { Subscriber } from '../Subscriber';
 import { SchedulerAction, SchedulerLike } from '../types';
 import { map } from '../operators/map';
+import { canReportError } from '../util/canReportError';
 import { isScheduler } from '../util/isScheduler';
 import { isArray } from '../util/isArray';
 
@@ -198,7 +199,11 @@ export function bindNodeCallback<T>(
           try {
             callbackFunc.apply(context, [...args, handler]);
           } catch (err) {
-            subject.error(err);
+            if (canReportError(subject)) {
+              subject.error(err);
+            } else {
+              console.warn(err);
+            }
           }
         }
         return subject.subscribe(subscriber);
diff --git a/src/internal/util/canReportError.ts b/src/internal/util/canReportError.ts
new file mode 100644
index 0000000000..caa98f7ea6
--- /dev/null
+++ b/src/internal/util/canReportError.ts
@@ -0,0 +1,22 @@
+import { isTrustedSubscriber, Subscriber } from '../Subscriber';
+import { Subject } from '../Subject';
+
+/**
+ * Determines whether the ErrorObserver is closed or stopped or has a
+ * destination that is closed or stopped - in which case errors will
+ * need to be reported via a different mechanism.
+ * @param observer the observer
+ */
+export function canReportError(observer: Subscriber<any> | Subject<any>): boolean {
+  while (observer) {
+    const { closed, destination, isStopped } = observer as any;
+    if (closed || isStopped) {
+      return false;
+    } else if (destination && isTrustedSubscriber(destination)) {
+      observer = destination;
+    } else {
+      observer = null;
+    }
+  }
+  return true;
+}