In recent years there has been an increasing interest in extensions of the logic programming paradigm beyond the class of normal logic programs motivated by the need for a satisfactory respresentation and processing of knowledge. An important problem in this area is to find an adequate declarative semantics for logic programs. In the present paper a general preference criterion is proposed that selects the ‘intended’ partial models of extended generalized logic programs which is a conservative extension of the stationary semantics for normal logic programs of [13], [14] and generalizes the WFSX-semantics of [12]. The presented preference criterion defines a partial model of an extended generalized logic program as intended if it is generated by a stationary chain. The GWFSX-semantics is defined by the set-theoretical intersection of all stationary generated models, and thus generalizes the results from [9] and [1].