This paper addresses the problem of atomic multicasting messages in asynchronous systems with unreliable failure detection. First, we give a characterisation of the notion of algorithms tolerating unreliable failure detection. Second, we give a characterisation of the notion of genuine atomic multicast. This characterisation leads to a better understanding of the difference between atomic multicast and atomic broadcast, and to a clear distinction between genuine atomic multicast algorithms and non-genuine atomic multicast algorithms. Third, we show that in a system with at least three processes, the genuine atomic multicast problem cannot be solved with unreliable failure detection, if at least one process may crash. We mention however two ways of circumventing this impossibility result.