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Agreement problems, such as consensus, atomic broadcast, and group membership, are central to the implementation of fault-tolerant distributed systems. Despite the diversity of algorithms that have been proposed for solving agreement problems in the past years, almost all solutions are crash detection based (CDB). We say that an algorithm is CDB if it uses some information about the status crashed/not crashed of processes. Randomized consensus algorithms are rare exceptions non-CDB algorithms. In this paper, we revisit the issue of non-CDB algorithms. Instead of randomization, we consider ordering oracles. Ordering oracles have a theoretical interest (e.g., they extend the state of the art of non-CDB algorithms) as well as a practical interest (e.g., they remove altogether the burden involved in tuning timeout mechanisms). To illustrate their use, we present solutions to consensus and atomic broadcast, and evaluate the performance of the atomic broadcast algorithm in a cluster of workstations.