diff --git a/src/plumpy/rmq/communications.py b/src/plumpy/rmq/communications.py
index 188108be..9dbafbed 100644
--- a/src/plumpy/rmq/communications.py
+++ b/src/plumpy/rmq/communications.py
@@ -8,7 +8,7 @@
 import kiwipy
 
 from plumpy import futures
-from plumpy.rmq.futures import wrap_to_kiwi_future
+from plumpy.rmq.futures import wrap_to_concurrent_future
 from plumpy.utils import ensure_coroutine
 
 __all__ = [
@@ -72,7 +72,7 @@ def converted(communicator: kiwipy.Communicator, *args: Any, **kwargs: Any) -> k
 
         msg_fn = functools.partial(coro, communicator, *args, **kwargs)
         task_future = futures.create_task(msg_fn, loop)
-        return wrap_to_kiwi_future(task_future)
+        return wrap_to_concurrent_future(task_future)
 
     return converted
 
diff --git a/src/plumpy/rmq/futures.py b/src/plumpy/rmq/futures.py
index 649fb2b4..897c8147 100644
--- a/src/plumpy/rmq/futures.py
+++ b/src/plumpy/rmq/futures.py
@@ -1,23 +1,107 @@
 # -*- coding: utf-8 -*-
-"""
-Module containing future related methods and classes
-"""
+# mypy: disable-error-code="no-untyped-def, no-untyped-call"
+"""Module containing future related methods and classes"""
 
 import asyncio
 import concurrent.futures
-from asyncio.futures import _chain_future, _copy_future_state  # type: ignore[attr-defined]
 from typing import Any
 
 import kiwipy
 
-__all__ = ['chain', 'copy_future', 'wrap_to_kiwi_future']
+__all__ = ['wrap_to_concurrent_future']
 
-copy_future = _copy_future_state
-chain = _chain_future
 
+def _convert_future_exc(exc):
+    exc_class = type(exc)
+    if exc_class is concurrent.futures.CancelledError:
+        return asyncio.exceptions.CancelledError(*exc.args)
+    elif exc_class is concurrent.futures.TimeoutError:
+        return asyncio.exceptions.TimeoutError(*exc.args)
+    elif exc_class is concurrent.futures.InvalidStateError:
+        return asyncio.exceptions.InvalidStateError(*exc.args)
+    else:
+        return exc
 
-def wrap_to_kiwi_future(future: asyncio.Future[Any]) -> kiwipy.Future:
-    """Wrap to concurrent.futures.Future object."""
+
+def _set_concurrent_future_state(concurrent, source):
+    """Copy state from a future to a concurrent.futures.Future."""
+    assert source.done()
+    if source.cancelled():
+        concurrent.cancel()
+    if not concurrent.set_running_or_notify_cancel():
+        return
+    exception = source.exception()
+    if exception is not None:
+        concurrent.set_exception(_convert_future_exc(exception))
+    else:
+        result = source.result()
+        concurrent.set_result(result)
+
+
+def _copy_future_state(source, dest):
+    """Internal helper to copy state from another Future.
+
+    The other Future may be a concurrent.futures.Future.
+    """
+    assert source.done()
+    if dest.cancelled():
+        return
+    assert not dest.done()
+    if source.cancelled():
+        dest.cancel()
+    else:
+        exception = source.exception()
+        if exception is not None:
+            dest.set_exception(_convert_future_exc(exception))
+        else:
+            result = source.result()
+            dest.set_result(result)
+
+
+def _chain_future(source, destination):
+    """Chain two futures so that when one completes, so does the other.
+
+    The result (or exception) of source will be copied to destination.
+    If destination is cancelled, source gets cancelled too.
+    Compatible with both asyncio.Future and concurrent.futures.Future.
+    """
+    if not asyncio.isfuture(source) and not isinstance(source, concurrent.futures.Future):
+        raise TypeError('A future is required for source argument')
+    if not asyncio.isfuture(destination) and not isinstance(destination, concurrent.futures.Future):
+        raise TypeError('A future is required for destination argument')
+    source_loop = asyncio.Future.get_loop(source) if asyncio.isfuture(source) else None
+    dest_loop = asyncio.Future.get_loop(destination) if asyncio.isfuture(destination) else None
+
+    def _set_state(future, other):
+        if asyncio.isfuture(future):
+            _copy_future_state(other, future)
+        else:
+            _set_concurrent_future_state(future, other)
+
+    def _call_check_cancel(destination):
+        if destination.cancelled():
+            if source_loop is None or source_loop is dest_loop:
+                source.cancel()
+            else:
+                source_loop.call_soon_threadsafe(source.cancel)
+
+    def _call_set_state(source):
+        if destination.cancelled() and dest_loop is not None and dest_loop.is_closed():
+            return
+        if dest_loop is None or dest_loop is source_loop:
+            _set_state(destination, source)
+        else:
+            if dest_loop.is_closed():
+                return
+            dest_loop.call_soon_threadsafe(_set_state, destination, source)
+
+    destination.add_done_callback(_call_check_cancel)
+    source.add_done_callback(_call_set_state)
+
+
+def wrap_to_concurrent_future(future: asyncio.Future[Any]) -> kiwipy.Future:
+    """Wrap to concurrent.futures.Future object. (the function is adapted from asyncio.future.wrap_future).
+    The function `_chain_future`, `_copy_future_state` is from asyncio future module."""
     if isinstance(future, concurrent.futures.Future):
         return future
     assert asyncio.isfuture(future), f'concurrent.futures.Future is expected, got {future!r}'