We consider asynchronous distributed systems with message losses and process crashes. We study the impact of finite process memory on the solution to consensus, repeated consensus and reliable broadcast. With finite process memory, we show that in some sense consensus is easier to solve than reliable broadcast, and that reliable broadcast is as difficult to solve as repeated consensus: More precisely, with finite memory, consensus can be solved with failure detector S, and P(a variant of the perfect failure detector which is stronger than S) is necessary and sufficient to solve reliable broadcast and repeated consensus.