The present paper introduces a new kind of stability——strong stability with respect to part of the variables in systems with impulse effect. The question on the stability is discussed. Effective sufficient conditions are found for strong stability with respect to partial variables of the zero solution of an impulsive differential system. The approach present is based on the specially introduced piecewise continuous Lyapunov functions and two important lemmas. Finally the obtained criteria are applied to the investigation of strong stability of the zero solutions with respect to part of the variables in impulsive differential systems.