We present a general protocol for detecting whether a property holds in a distributed system, where the property is a member of a subclass of stable properties we call the locally stable properties. Our protocol is based on a decentralized method for constructing a maximal subset of the local states that are mutually consistent, which in turn is based on a weakened version of vector time stamps. The structure of our protocol lends itself to refinement, and we demonstrate its utility by deriving some specialized property-detection protocols, including two previously-known protocols that are known to be efficient.