 We introduce the concept of unreliable failure detectors 	and study how they can be used to solve Consensus 	in asynchronous systems	with crash failures. We characterise unreliable failure detectors  	in terms of two properties --- 	completeness and accuracy. We show that Consensus can be solved even with unreliable failure detectors 	that make an infinite number of mistakes, 	and determine which ones 	can be used to solve Consensus 	despite any number of crashes, 	and which ones require a majority of correct processes. We prove that Consensus and Atomic Broadcast are reducible to 	each other in asynchronous systems with crash failures; 	thus the above results also apply to Atomic Broadcast. A companion paper shows that one of the failure detectors introduced here 	is the weakest failure detector for solving Consensus <a href="http://www.cs.cornell.edu/Info/People/chandra/WeakestFD.html">[CHT92]</a>. <hr> Research supported by an IBM graduate fellowship, NSF grants CCR-8901780 and 	CCR-9102231, DARPA/NASA Ames Grant NAG-2-593, and in part by Grants 	from IBM and Siemens Corp. <hr> <i>Maintained by <a href="http://www.cs.cornell.edu/Info/People/chandra/home.html">tushar@watson.ibm.com</a></i>
