diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index 6226bbf5eb4063..1e42b15363fb36 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -140,6 +140,9 @@ function ReadableState(options, stream, isDuplex) {
   // Has it been destroyed
   this.destroyed = false;
 
+  // Indicates whether the stream has errored.
+  this.errored = false;
+
   // Crypto is kind of old and crusty.  Historically, its default string
   // encoding is 'binary' so we have to make this configurable.
   // Everything else in the universe uses 'utf8', though.
diff --git a/lib/internal/streams/destroy.js b/lib/internal/streams/destroy.js
index ded75b255934c4..fb206c6c83d0a0 100644
--- a/lib/internal/streams/destroy.js
+++ b/lib/internal/streams/destroy.js
@@ -1,41 +1,25 @@
 'use strict';
 
-function needError(stream, err) {
-  if (!err) {
-    return false;
-  }
-
-  const r = stream._readableState;
-  const w = stream._writableState;
-
-  if ((w && w.errorEmitted) || (r && r.errorEmitted)) {
-    return false;
-  }
-
-  if (w) {
-    w.errorEmitted = true;
-  }
-  if (r) {
-    r.errorEmitted = true;
-  }
-
-  return true;
-}
-
 // Undocumented cb() API, needed for core, not for public API.
 // The cb() will be invoked synchronously if _destroy is synchronous.
+// If cb is passed no 'error' event will be emitted.
 function destroy(err, cb) {
   const r = this._readableState;
   const w = this._writableState;
 
-  if (w && err) {
-    w.errored = true;
+  if (err) {
+    if (w) {
+      w.errored = true;
+    }
+    if (r) {
+      r.errored = true;
+    }
   }
 
   if ((w && w.destroyed) || (r && r.destroyed)) {
     if (cb) {
       cb(err);
-    } else if (needError(this, err)) {
+    } else if (err) {
       process.nextTick(emitErrorNT, this, err);
     }
 
@@ -53,17 +37,24 @@ function destroy(err, cb) {
   }
 
   this._destroy(err || null, (err) => {
-    const emitClose = (w && w.emitClose) || (r && r.emitClose);
+    if (err) {
+      if (w) {
+        w.errored = true;
+      }
+      if (r) {
+        r.errored = true;
+      }
+    }
+
     if (cb) {
       // Invoke callback before scheduling emitClose so that callback
       // can schedule before.
       cb(err);
-      if (emitClose) {
-        process.nextTick(emitCloseNT, this);
-      }
-    } else if (needError(this, err)) {
-      process.nextTick(emitClose ? emitErrorCloseNT : emitErrorNT, this, err);
-    } else if (emitClose) {
+      // Don't emit 'error' if passed a callback.
+      process.nextTick(emitCloseNT, this);
+    } else if (err) {
+      process.nextTick(emitErrorCloseNT, this, err);
+    } else {
       process.nextTick(emitCloseNT, this);
     }
   });
@@ -72,15 +63,34 @@ function destroy(err, cb) {
 }
 
 function emitErrorCloseNT(self, err) {
-  self.emit('error', err);
-  self.emit('close');
+  emitErrorNT(self, err);
+  emitCloseNT(self);
 }
 
 function emitCloseNT(self) {
-  self.emit('close');
+  const r = self._readableState;
+  const w = self._writableState;
+
+  if ((w && w.emitClose) || (r && r.emitClose)) {
+    self.emit('close');
+  }
 }
 
 function emitErrorNT(self, err) {
+  const r = self._readableState;
+  const w = self._writableState;
+
+  if ((w && w.errorEmitted) || (r && r.errorEmitted)) {
+    return;
+  }
+
+  if (w) {
+    w.errorEmitted = true;
+  }
+  if (r) {
+    r.errorEmitted = true;
+  }
+
   self.emit('error', err);
 }
 
@@ -90,6 +100,7 @@ function undestroy() {
 
   if (r) {
     r.destroyed = false;
+    r.errored = false;
     r.reading = false;
     r.ended = false;
     r.endEmitted = false;
@@ -118,14 +129,17 @@ function errorOrDestroy(stream, err) {
   const r = stream._readableState;
   const w = stream._writableState;
 
-  if (w & err) {
-    w.errored = true;
-  }
-
   if ((r && r.autoDestroy) || (w && w.autoDestroy))
     stream.destroy(err);
-  else if (needError(stream, err))
-    stream.emit('error', err);
+  else if (err) {
+    if (w) {
+      w.errored = true;
+    }
+    if (r) {
+      r.errored = true;
+    }
+    emitErrorNT(stream, err);
+  }
 }
 
 
diff --git a/test/parallel/test-stream-readable-destroy.js b/test/parallel/test-stream-readable-destroy.js
index 7687ea90cc82d8..d446dd3611781e 100644
--- a/test/parallel/test-stream-readable-destroy.js
+++ b/test/parallel/test-stream-readable-destroy.js
@@ -129,13 +129,20 @@ const assert = require('assert');
     cb(expected);
   });
 
+  let ticked = false;
   read.on('end', common.mustNotCall('no end event'));
   read.on('error', common.mustCall((err) => {
+    assert.strictEqual(ticked, true);
+    assert.strictEqual(read._readableState.errorEmitted, true);
+    assert.strictEqual(read._readableState.errored, true);
     assert.strictEqual(err, expected);
   }));
 
   read.destroy();
+  assert.strictEqual(read._readableState.errorEmitted, false);
+  assert.strictEqual(read._readableState.errored, true);
   assert.strictEqual(read.destroyed, true);
+  ticked = true;
 }
 
 {
@@ -174,10 +181,58 @@ const assert = require('assert');
 
   const expected = new Error('kaboom');
 
-  read.on('close', common.mustCall());
+  let ticked = false;
+  read.on('close', common.mustCall(() => {
+    assert.strictEqual(read._readableState.errorEmitted, false);
+    assert.strictEqual(ticked, true);
+  }));
+  // 'error' should not be emitted since a callback is passed to
+  // destroy(err, callback);
+  read.on('error', common.mustNotCall());
+
+  assert.strictEqual(read._readableState.errored, false);
+  assert.strictEqual(read._readableState.errorEmitted, false);
+
   read.destroy(expected, common.mustCall(function(err) {
+    assert.strictEqual(read._readableState.errored, true);
     assert.strictEqual(err, expected);
   }));
+  assert.strictEqual(read._readableState.errorEmitted, false);
+  assert.strictEqual(read._readableState.errored, true);
+  ticked = true;
+}
+
+{
+  const readable = new Readable({
+    destroy: common.mustCall(function(err, cb) {
+      process.nextTick(cb, new Error('kaboom 1'));
+    }),
+    read() {}
+  });
+
+  let ticked = false;
+  readable.on('close', common.mustCall(() => {
+    assert.strictEqual(ticked, true);
+    assert.strictEqual(readable._readableState.errorEmitted, true);
+  }));
+  readable.on('error', common.mustCall((err) => {
+    assert.strictEqual(ticked, true);
+    assert.strictEqual(err.message, 'kaboom 2');
+    assert.strictEqual(readable._readableState.errorEmitted, true);
+  }));
+
+  readable.destroy();
+  assert.strictEqual(readable.destroyed, true);
+  assert.strictEqual(readable._readableState.errored, false);
+  assert.strictEqual(readable._readableState.errorEmitted, false);
+
+  // Test case where `readable.destroy()` is called again with an error before
+  // the `_destroy()` callback is called.
+  readable.destroy(new Error('kaboom 2'));
+  assert.strictEqual(readable._readableState.errorEmitted, false);
+  assert.strictEqual(readable._readableState.errored, true);
+
+  ticked = true;
 }
 
 {
diff --git a/test/parallel/test-stream-writable-destroy.js b/test/parallel/test-stream-writable-destroy.js
index 1186c618634cab..d321d808199d56 100644
--- a/test/parallel/test-stream-writable-destroy.js
+++ b/test/parallel/test-stream-writable-destroy.js
@@ -157,13 +157,22 @@ const assert = require('assert');
     write(chunk, enc, cb) { cb(); }
   });
 
-  write.on('close', common.mustCall());
-  write.on('error', common.mustCall());
+  let ticked = false;
+  write.on('close', common.mustCall(() => {
+    assert.strictEqual(ticked, true);
+  }));
+  write.on('error', common.mustCall((err) => {
+    assert.strictEqual(ticked, true);
+    assert.strictEqual(err.message, 'kaboom 1');
+    assert.strictEqual(write._writableState.errorEmitted, true);
+  }));
 
   write.destroy(new Error('kaboom 1'));
   write.destroy(new Error('kaboom 2'));
-  assert.strictEqual(write._writableState.errorEmitted, true);
+  assert.strictEqual(write._writableState.errored, true);
+  assert.strictEqual(write._writableState.errorEmitted, false);
   assert.strictEqual(write.destroyed, true);
+  ticked = true;
 }
 
 {
@@ -176,20 +185,29 @@ const assert = require('assert');
     }
   });
 
-  writable.on('close', common.mustCall());
-  writable.on('error', common.expectsError({
-    type: Error,
-    message: 'kaboom 2'
+  let ticked = false;
+  writable.on('close', common.mustCall(() => {
+    assert.strictEqual(ticked, true);
+    assert.strictEqual(writable._writableState.errorEmitted, true);
+  }));
+  writable.on('error', common.mustCall((err) => {
+    assert.strictEqual(ticked, true);
+    assert.strictEqual(err.message, 'kaboom 2');
+    assert.strictEqual(writable._writableState.errorEmitted, true);
   }));
 
   writable.destroy();
   assert.strictEqual(writable.destroyed, true);
+  assert.strictEqual(writable._writableState.errored, false);
   assert.strictEqual(writable._writableState.errorEmitted, false);
 
   // Test case where `writable.destroy()` is called again with an error before
   // the `_destroy()` callback is called.
   writable.destroy(new Error('kaboom 2'));
-  assert.strictEqual(writable._writableState.errorEmitted, true);
+  assert.strictEqual(writable._writableState.errorEmitted, false);
+  assert.strictEqual(writable._writableState.errored, true);
+
+  ticked = true;
 }
 
 {