RESUMEN

            We have considered the complete integrability of two nonlinear equations which are some kind of extensions of usual Sine-Gordon equations. The first one is of non-autonomous version of Sine-Gordon system and the second is closely related to the usual Sine-Gordon theory. The first problem indicates how (x,t) dependent non-linear equations can be treated in the prolongation theory and how a Backlund map can be constructed. The Second one is a variation of the usual Sine-Gordon equation and suggests that there may be other equations (similar to Sine-Gordon) which are completely integrable. In both the case be have been able to construct the lax pair. We then construct an auto-Backlund map by following the idea of Konno and Wadati, for the generation of multisolution states.