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Failure detection and group membership are two important components of fault-tolerant distributed systems. Understanding their role is essential when developing efficient solutions, not only in failure-free runs, but also in runs in which processes do crash. While group membership provides consistent information about the status of processes in the system, failure detectors provide inconsistent information. This paper discusses the trade-offs related to the use of these two components, and clarifies their roles using three examples. The first example shows a case where group membership may favourably be replaced by a failure detection mechanism. The second example illustrates a case where group membership is mandatory. Finally, the third example shows a case where neither group membership nor failure detectors are needed (they may be replaced by weak ordering oracles).