In this paper we analyze declarative deterministic and non-deterministic semantics for active rules. In particular, we consider several (partial) stable model semantics, previously defined for deductive rules, such as well-founded, max deterministic, unique total stable model, total stable model and maximal stable model semantics. The semantics of an active program [Ascr ][Pscr ] is given by first rewriting it into a deductive program [Lscr ][Pscr ], then computing a model M defining the declarative semantics of [Lscr ][Pscr ] and, finally, applying ‘consistent’ updates contained in M to the source database. The framework we propose permits a natural integration of deductive and active rules and can also be applied to queries with function symbols or to queries over infinite databases.