diff --git a/lib/net.js b/lib/net.js
index 7f6f306b846..620fd29a321 100644
--- a/lib/net.js
+++ b/lib/net.js
@@ -249,9 +249,11 @@ function onSocketEnd() {
   this._readableState.ended = true;
   if (this._readableState.endEmitted) {
     this.readable = false;
+    maybeDestroy(this);
   } else {
     this.once('end', function() {
       this.readable = false;
+      maybeDestroy(this);
     });
     this.read(0);
   }
@@ -399,10 +401,22 @@ Socket.prototype.end = function(data, encoding) {
   // just in case we're waiting for an EOF.
   if (this.readable && !this._readableState.endEmitted)
     this.read(0);
-  return;
+  else
+    maybeDestroy(this);
 };
 
 
+// Call whenever we set writable=false or readable=false
+function maybeDestroy(socket) {
+  if (!socket.readable &&
+      !socket.writable &&
+      !socket.destroyed &&
+      !socket._connecting) {
+    socket.destroy();
+  }
+}
+
+
 Socket.prototype.destroySoon = function() {
   if (this.writable)
     this.end();
@@ -521,8 +535,10 @@ function onread(buffer, offset, length) {
   } else if (process._errno == 'EOF') {
     debug('EOF');
 
-    if (self._readableState.length === 0)
+    if (self._readableState.length === 0) {
       self.readable = false;
+      maybeDestroy(self);
+    }
 
     if (self.onend) self.once('end', self.onend);
 
diff --git a/test/simple/test-net-GH-5504.js b/test/simple/test-net-GH-5504.js
new file mode 100644
index 00000000000..d5059f02864
--- /dev/null
+++ b/test/simple/test-net-GH-5504.js
@@ -0,0 +1,123 @@
+// Copyright Joyent, Inc. and other Node contributors.
+//
+// Permission is hereby granted, free of charge, to any person obtaining a
+// copy of this software and associated documentation files (the
+// "Software"), to deal in the Software without restriction, including
+// without limitation the rights to use, copy, modify, merge, publish,
+// distribute, sublicense, and/or sell copies of the Software, and to permit
+// persons to whom the Software is furnished to do so, subject to the
+// following conditions:
+//
+// The above copyright notice and this permission notice shall be included
+// in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
+// NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+// DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
+// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
+// USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+var common = require('../common');
+var assert = require('assert');
+
+// this test only fails with CentOS 6.3 using kernel version 2.6.32
+// On other linuxes and darwin, the `read` call gets an ECONNRESET in
+// that case.  On sunos, the `write` call fails with EPIPE.
+//
+// However, old CentOS will occasionally send an EOF instead of a
+// ECONNRESET or EPIPE when the client has been destroyed abruptly.
+//
+// Make sure we don't keep trying to write or read more in that case.
+
+switch (process.argv[2]) {
+  case 'server': return server();
+  case 'client': return client();
+  case undefined: return parent();
+  default: throw new Error('wtf');
+}
+
+function server() {
+  var net = require('net');
+  var content = new Buffer(64 * 1024 * 1024);
+  content.fill('#');
+  net.createServer(function(socket) {
+    this.close();
+    socket.on('end', function() {
+      console.error('end');
+    });
+    socket.on('_socketEnd', function() {
+      console.error('_socketEnd');
+    });
+    socket.write(content);
+  }).listen(3000, function() {
+    console.log('listening');
+  });
+}
+
+function client() {
+  var net = require('net');
+  var client = net.connect({
+    host: 'localhost',
+    port: 3000
+  }, function() {
+    client.destroy();
+  });
+}
+
+function parent() {
+  var spawn = require('child_process').spawn;
+  var node = process.execPath;
+  var assert = require('assert');
+  var serverExited = false;
+  var clientExited = false;
+  var serverListened = false;
+  var opt = { env: { NODE_DEBUG: 'net' } };
+
+  process.on('exit', function() {
+    assert(serverExited);
+    assert(clientExited);
+    assert(serverListened);
+    console.log('ok');
+  });
+
+  setTimeout(function() {
+    if (s) s.kill();
+    if (c) c.kill();
+    setTimeout(function() {
+      throw new Error('hang');
+    });
+  }, 1000).unref();
+
+  var s = spawn(node, [__filename, 'server'], opt);
+  var c;
+
+  wrap(s.stderr, process.stderr, 'SERVER 2>');
+  wrap(s.stdout, process.stdout, 'SERVER 1>');
+  s.on('exit', function(c) {
+    console.error('server exited', c);
+    serverExited = true;
+  });
+
+  s.stdout.once('data', function() {
+    serverListened = true;
+    c = spawn(node, [__filename, 'client']);
+    wrap(c.stderr, process.stderr, 'CLIENT 2>');
+    wrap(c.stdout, process.stdout, 'CLIENT 1>');
+    c.on('exit', function(c) {
+      console.error('client exited', c);
+      clientExited = true;
+    });
+  });
+
+  function wrap(inp, out, w) {
+    inp.setEncoding('utf8');
+    inp.on('data', function(c) {
+      c = c.trim();
+      if (!c) return;
+      out.write(w + c.split('\n').join('\n' + w) + '\n');
+    });
+  }
+}
+