diff --git a/src/asynkit/coroutine.py b/src/asynkit/coroutine.py
index 850f2e2..3c88c77 100644
--- a/src/asynkit/coroutine.py
+++ b/src/asynkit/coroutine.py
@@ -108,7 +108,10 @@ def coro_is_new(coro: Suspendable) -> bool:
     elif inspect.isgenerator(coro):
         return inspect.getgeneratorstate(coro) == inspect.GEN_CREATED
     elif inspect.isasyncgen(coro):
-        return coro.ag_frame is not None and not coro.ag_running
+        # async generators have an ag_await if they are suspended
+        # ag_running() means that it is inside an anext() or athrow()
+        # but it may be suspended.
+        return coro.ag_frame is not None and coro.ag_await is None and not coro.ag_running
     else:
         raise TypeError(
             f"a coroutine or coroutine like object is required. Got: {type(coro)}"
@@ -124,9 +127,7 @@ def coro_is_suspended(coro: Suspendable) -> bool:
     elif inspect.isgenerator(coro):
         return inspect.getgeneratorstate(coro) == inspect.GEN_SUSPENDED
     elif inspect.isasyncgen(coro):
-        # This is true only if we are inside an anext() or athrow(), not if the
-        # inner coroutine is itself doing an await before yielding a value.
-        return coro.ag_running
+        return coro.ag_await is not None
     else:
         raise TypeError(
             f"a coroutine or coroutine like object is required. Got: {type(coro)}"