diff --git a/libp2p/stream_muxer/mplex/mplex.py b/libp2p/stream_muxer/mplex/mplex.py
index 95336d9..ecddedd 100644
--- a/libp2p/stream_muxer/mplex/mplex.py
+++ b/libp2p/stream_muxer/mplex/mplex.py
@@ -1,5 +1,5 @@
 import asyncio
-from typing import Dict, Tuple
+from typing import Dict, Tuple, Optional
 
 from multiaddr import Multiaddr
 
@@ -10,6 +10,7 @@ from libp2p.security.secure_conn_interface import ISecureConn
 from libp2p.stream_muxer.abc import IMuxedConn, IMuxedStream
 
 from .constants import HeaderTags
+from .exceptions import StreamNotFound
 from .mplex_stream import MplexStream
 from .utils import decode_uvarint_from_stream, encode_uvarint
 
@@ -23,6 +24,9 @@ class Mplex(IMuxedConn):
     raw_conn: IRawConnection
     initiator: bool
     peer_id: ID
+    # TODO: `dataIn` in go implementation. Should be size of 8.
+    # TODO: Also, `dataIn` is closed indicating EOF in Go. We don't have similar strategies
+    #   to let the `MplexStream`s know that EOF arrived (#235).
     buffers: Dict[int, "asyncio.Queue[bytes]"]
     stream_queue: "asyncio.Queue[int]"
 
@@ -75,17 +79,19 @@ class Mplex(IMuxedConn):
         :param stream_id: stream id of stream to read from
         :return: message read
         """
-        # TODO: propagate up timeout exception and catch
-        # TODO: pass down timeout from user and use that
-        if stream_id in self.buffers:
-            try:
-                data = await asyncio.wait_for(self.buffers[stream_id].get(), timeout=8)
-                return data
-            except asyncio.TimeoutError:
-                return None
+        if stream_id not in self.buffers:
+            raise StreamNotFound(f"stream {stream_id} is not found")
+        return await self.buffers[stream_id].get()
 
-        # Stream not created yet
-        return None
+    async def read_buffer_nonblocking(self, stream_id: int) -> Optional[bytes]:
+        """
+        Read a message from `stream_id`'s buffer, non-blockingly.
+        """
+        if stream_id not in self.buffers:
+            raise StreamNotFound(f"stream {stream_id} is not found")
+        if self.buffers[stream_id].empty():
+            return None
+        return await self.buffers[stream_id].get()
 
     async def open_stream(
         self, protocol_id: str, multi_addr: Multiaddr
@@ -170,6 +176,7 @@ class Mplex(IMuxedConn):
         :return: stream_id, flag, message contents
         """
 
+        # FIXME: No timeout is used in Go implementation.
         # Timeout is set to a relatively small value to alleviate wait time to exit
         #  loop in handle_incoming
         timeout = 0.1
diff --git a/libp2p/stream_muxer/mplex/mplex_stream.py b/libp2p/stream_muxer/mplex/mplex_stream.py
index 6df8227..afc49ee 100644
--- a/libp2p/stream_muxer/mplex/mplex_stream.py
+++ b/libp2p/stream_muxer/mplex/mplex_stream.py
@@ -37,33 +37,31 @@ class MplexStream(IMuxedStream):
         self.local_closed = False
         self.remote_closed = False
         self.stream_lock = asyncio.Lock()
-        self._buf = None
+        self._buf = b""
 
-    async def read(self, n: int = -1) -> bytes:
+    async def read(self, n) -> bytes:
         """
-        read messages associated with stream from buffer til end of file
+        Read up to n bytes. Read possibly returns fewer than `n` bytes,
+        if there are not enough bytes in the Mplex buffer.
         :param n: number of bytes to read
-        :return: bytes of input
+        :return: bytes actually read
         """
-        if n == -1:
-            return await self.mplex_conn.read_buffer(self.stream_id)
-        return await self.read_bytes(n)
-
-    async def read_bytes(self, n: int) -> bytes:
-        if self._buf is None:
+        # If the buffer is empty at first, blocking wait for data.
+        if len(self._buf) == 0:
             self._buf = await self.mplex_conn.read_buffer(self.stream_id)
-        n_read = 0
-        bytes_buf = BytesIO()
-        while self._buf is not None and n_read < n:
-            n_to_read = min(n - n_read, len(self._buf))
-            bytes_buf.write(self._buf[:n_to_read])
-            if n_to_read == n - n_read:
-                self._buf = self._buf[n_to_read:]
-            else:
-                self._buf = None
-                self._buf = await self.mplex_conn.read_buffer(self.stream_id)
-            n_read += n_to_read
-        return bytes_buf.getvalue()
+        # Here, `self._buf` should never be `None`.
+        if self._buf is None or len(self._buf) == 0:
+            raise Exception("start to `read_buffer_nonblocking` only when there are bytes read.")
+
+        while len(self._buf) < n:
+            new_bytes = await self.mplex_conn.read_buffer_nonblocking(self.stream_id)
+            if new_bytes is None:
+                # Nothing to read in the `MplexConn` buffer
+                break
+            self._buf += new_bytes
+        payload = self._buf[:n]
+        self._buf = self._buf[n:]
+        return payload
 
     async def write(self, data: bytes) -> int:
         """