A stable property in a distributed system is a global property which once true, remains true forever. This paper refines this notion by formally introducing the concept of ``strong'' stable properties. A strong stable property has the nice property that it can be correctly evaluated on the consistent part of uncoordinated snapshots. Termination and deadlock are shown to be strong stable properties, whereas garbage is not. We also show how to derive a simple generic algorithm for the detection of a strong stable property. The generic algorithm is illustrated by two examples: termination detection and deadlock detection. Incidentally the paper presents a very simple algorithm for termination detection.