diff --git a/test/functional/abc-invalid-message.py b/test/functional/abc-invalid-message.py
--- a/test/functional/abc-invalid-message.py
+++ b/test/functional/abc-invalid-message.py
@@ -22,7 +22,7 @@
 
 
 def msg_bad_checksum(connection, original_message):
-    message_data = bytearray(connection._build_message(original_message))
+    message_data = bytearray(connection.build_message(original_message))
 
     data = original_message.serialize()
     i = 0
diff --git a/test/functional/p2p_invalid_messages.py b/test/functional/p2p_invalid_messages.py
new file mode 100755
--- /dev/null
+++ b/test/functional/p2p_invalid_messages.py
@@ -0,0 +1,180 @@
+#!/usr/bin/env python3
+# Copyright (c) 2015-2018 The Bitcoin Core developers
+# Distributed under the MIT software license, see the accompanying
+# file COPYING or http://www.opensource.org/licenses/mit-license.php.
+"""Test node responses to invalid network messages."""
+import struct
+
+from test_framework import messages
+from test_framework.mininode import P2PDataStore
+from test_framework.test_framework import BitcoinTestFramework
+
+
+class msg_unrecognized:
+    """Nonsensical message. Modeled after similar types in test_framework.messages."""
+
+    command = b'badmsg'
+
+    def __init__(self, str_data):
+        self.str_data = str_data.encode() if not isinstance(str_data, bytes) else str_data
+
+    def serialize(self):
+        return messages.ser_string(self.str_data)
+
+    def __repr__(self):
+        return "{}(data={})".format(self.command, self.str_data)
+
+
+class msg_nametoolong(msg_unrecognized):
+
+    command = b'thisnameiswayyyyyyyyytoolong'
+
+
+class InvalidMessagesTest(BitcoinTestFramework):
+
+    def set_test_params(self):
+        self.num_nodes = 1
+        self.setup_clean_chain = True
+
+    def run_test(self):
+        """
+        0. Send a bunch of large (2MB) messages of an unrecognized type. Check to see
+           that it isn't an effective DoS against the node.
+
+        1. Send an oversized (2MB+) message and check that we're disconnected.
+
+        2. Send a few messages with an incorrect data size in the header, ensure the
+           messages are ignored.
+
+        3. Send an unrecognized message with a command name longer than 12 characters.
+
+        """
+        node = self.nodes[0]
+        self.node = node
+        node.add_p2p_connection(P2PDataStore())
+        conn2 = node.add_p2p_connection(P2PDataStore())
+
+        # 2MB, per MAX_PROTOCOL_MESSAGE_LENGTH
+        msg_limit = 2 * 1024 * 1024
+        # Account for the 4-byte length prefix
+        valid_data_limit = msg_limit - 5
+
+        #
+        # 0.
+        #
+        # Send as large a message as is valid, ensure we aren't disconnected but
+        # also can't exhaust resources.
+        #
+        msg_at_size = msg_unrecognized("b" * valid_data_limit)
+        assert len(msg_at_size.serialize()) == msg_limit
+
+        with node.assert_memory_usage_stable(perc_increase_allowed=0.03):
+            self.log.info(
+                "Sending a bunch of large, junk messages to test "
+                "memory exhaustion. May take a bit...")
+
+            # Run a bunch of times to test for memory exhaustion.
+            for _ in range(80):
+                node.p2p.send_message(msg_at_size)
+
+            # Check that, even though the node is being hammered by nonsense from one
+            # connection, it can still service other peers in a timely way.
+            for _ in range(20):
+                conn2.sync_with_ping(timeout=2)
+
+            # Peer 1, despite serving up a bunch of nonsense, should still be
+            # connected.
+            self.log.info("Waiting for node to drop junk messages.")
+            node.p2p.sync_with_ping(timeout=30)
+            assert node.p2p.is_connected
+
+        #
+        # 1.
+        #
+        # Send an oversized message, ensure we're disconnected.
+        #
+        msg_over_size = msg_unrecognized("b" * (valid_data_limit + 1))
+        assert len(msg_over_size.serialize()) == (msg_limit + 1)
+
+        with node.assert_debug_log(["Oversized header detected"]):
+            # An unknown message type (or *any* message type) over
+            # MAX_PROTOCOL_MESSAGE_LENGTH should result in a disconnect.
+            node.p2p.send_message(msg_over_size)
+            node.p2p.wait_for_disconnect(timeout=4)
+
+        node.disconnect_p2ps()
+        conn = node.add_p2p_connection(P2PDataStore())
+        conn.wait_for_verack()
+
+        #
+        # 2.
+        #
+        # Send messages with an incorrect data size in the header.
+        #
+        actual_size = 100
+        msg = msg_unrecognized("b" * actual_size)
+
+        # TODO: handle larger-than cases. I haven't been able to pin down what
+        # behavior to expect.
+        for wrong_size in (2, 77, 78, 79):
+            self.log.info(
+                "Sending a message with incorrect size of {}".format(wrong_size))
+
+            # Unmodified message should submit okay.
+            node.p2p.send_and_ping(msg)
+
+            # A message lying about its data size results in a disconnect when the incorrect
+            # data size is less than the actual size.
+            #
+            # TODO: why does behavior change at 78 bytes?
+            #
+            node.p2p.send_raw_message(
+                self._tweak_msg_data_size(
+                    msg, wrong_size))
+
+            # For some reason unknown to me, we sometimes have to push additional data to the
+            # peer in order for it to realize a disconnect.
+            try:
+                node.p2p.send_message(messages.msg_ping(nonce=123123))
+            except IOError:
+                pass
+
+            node.p2p.wait_for_disconnect(timeout=10)
+            node.disconnect_p2ps()
+            node.add_p2p_connection(P2PDataStore())
+
+        #
+        # 3.
+        #
+        # Send a message with a too-long command name.
+        #
+        node.p2p.send_message(msg_nametoolong("foobar"))
+        node.p2p.wait_for_disconnect(timeout=4)
+
+        # Node is still up.
+        conn = node.add_p2p_connection(P2PDataStore())
+        conn.sync_with_ping()
+
+    def _tweak_msg_data_size(self, message, wrong_size):
+        """
+        Return a raw message based on another message but with an incorrect data size in
+        the message header.
+        """
+        raw_msg = self.node.p2p.build_message(message)
+
+        bad_size_bytes = struct.pack("<I", wrong_size)
+        num_header_bytes_before_size = 4 + 12
+
+        # Replace the correct data size in the message with an incorrect one.
+        raw_msg_with_wrong_size = (
+            raw_msg[:num_header_bytes_before_size] +
+            bad_size_bytes +
+            raw_msg[(num_header_bytes_before_size + len(bad_size_bytes)):]
+        )
+        assert len(raw_msg) == len(raw_msg_with_wrong_size)
+
+        return raw_msg_with_wrong_size
+
+
+if __name__ == '__main__':
+    InvalidMessagesTest().main()
diff --git a/test/functional/test_framework/mininode.py b/test/functional/test_framework/mininode.py
--- a/test/functional/test_framework/mininode.py
+++ b/test/functional/test_framework/mininode.py
@@ -234,11 +234,11 @@
         the message to the send buffer to be sent over the socket."""
         if not self.is_connected:
             raise IOError('Not connected')
+        tmsg = self.build_message(message)
         self._log_message("send", message)
-        tmsg = self._build_message(message)
-        self.send_raw_message(tmsg)
+        return self.send_raw_message(tmsg)
 
-    def send_raw_message(self, tmsg):
+    def send_raw_message(self, raw_message_bytes):
         """Send any raw message over the socket.
 
         This method adds a raw message to the send buffer to be sent over the
@@ -251,12 +251,12 @@
                 return
             if self._transport.is_closing():
                 return
-            self._transport.write(tmsg)
+            self._transport.write(raw_message_bytes)
         NetworkThread.network_event_loop.call_soon_threadsafe(maybe_write)
 
     # Class utility methods
 
-    def _build_message(self, message):
+    def build_message(self, message):
         """Build a serialized P2P message"""
         command = message.command
         data = message.serialize()
@@ -470,9 +470,9 @@
 
     # Message sending helper functions
 
-    def send_and_ping(self, message):
+    def send_and_ping(self, message, timeout=60):
         self.send_message(message)
-        self.sync_with_ping()
+        self.sync_with_ping(timeout=timeout)
 
     # Sync up with the node
     def sync_with_ping(self, timeout=60):
diff --git a/test/functional/test_framework/test_node.py b/test/functional/test_framework/test_node.py
--- a/test/functional/test_framework/test_node.py
+++ b/test/functional/test_framework/test_node.py
@@ -165,6 +165,29 @@
         assert len(self.PRIV_KEYS) == MAX_NODES
         return self.PRIV_KEYS[self.index]
 
+    def get_mem_rss(self):
+        """Get the memory usage (RSS) per `ps`.
+
+        If process is stopped or `ps` is unavailable, return None.
+        """
+        if not (self.running and self.process):
+            self.log.warning(
+                "Couldn't get memory usage; process isn't running.")
+            return None
+
+        try:
+            return int(subprocess.check_output(
+                "ps h -o rss {}".format(self.process.pid),
+                shell=True, stderr=subprocess.DEVNULL).strip())
+
+        # Catching `Exception` broadly to avoid failing on platforms where ps
+        # isn't installed or doesn't work as expected, e.g. OpenBSD.
+        #
+        # We could later use something like `psutils` to work across platforms.
+        except Exception:
+            self.log.exception("Unable to get memory usage")
+            return None
+
     def _node_msg(self, msg: str) -> str:
         """Return a modified msg that identifies this node by its index as a debugging aid."""
         return "[node {}] {}".format(self.index, msg)
@@ -402,6 +425,31 @@
             'Expected messages "{}" does not partially match log:\n\n{}\n\n'.format(
                 str(expected_msgs), print_log))
 
+    @contextlib.contextmanager
+    def assert_memory_usage_stable(self, perc_increase_allowed=0.03):
+        """Context manager that allows the user to assert that a node's memory usage (RSS)
+        hasn't increased beyond some threshold percentage.
+        """
+        before_memory_usage = self.get_mem_rss()
+
+        yield
+
+        after_memory_usage = self.get_mem_rss()
+
+        if not (before_memory_usage and after_memory_usage):
+            self.log.warning(
+                "Unable to detect memory usage (RSS) - skipping memory check.")
+            return
+
+        perc_increase_memory_usage = 1 - \
+            (float(before_memory_usage) / after_memory_usage)
+
+        if perc_increase_memory_usage > perc_increase_allowed:
+            self._raise_assertion_error(
+                "Memory usage increased over threshold of {:.3f}% from {} to {} ({:.3f}%)".format(
+                    perc_increase_allowed * 100, before_memory_usage, after_memory_usage,
+                    perc_increase_memory_usage * 100))
+
     def assert_start_raises_init_error(
             self, extra_args=None, expected_msg=None, match=ErrorMatch.FULL_TEXT, *args, **kwargs):
         """Attempt to start the node and expect it to raise an error.