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When evaluated to true, a stable property remains true forever. Such a stable property may characterize important states of a computation. This is the case of deadlocked or terminated computations. In this paper we expose a general algorithm for the distributed detection of stable properties in distributed applications or systems. This distributed algorithm deals with every stable property of a fairly general class: in this sense the algorithm is generic. This was achieved using a methodical approach, with a strong distinction between the computation and control activities in the problem. Moreover, the detection method used by the algorithm is based on an observational mechanism,