Impulsive di erential equations arise frequently in the modelling of many physical systems whose states are subjects to sudden change at certain moments, for example, in population biology, the di usion of chemicals, the spread of heat, the radiation of electromagnetic waves, the maintenance of a species through instantaneous stocking and harvesing, etc. There has been an increasing interest in the investigation for such equations during the past few years. The stability theory for impulsive di erential equations employing discontinuous Lyapunov functions has been developed intensively. We mention here the works [1,2,4 -6]. However, the qualitative theory for impulsive di erential equations is still in an initial stage of its development. It is noted that impulsive autonomous systems with ΓΏxed moments of impulsive e ects are ΓΏrst investigated in [3] where necessary and su cient conditions for the existence of period orbit are established. In this paper we shall investigate the qualitative properties of impulsive di erential equations with impulses at variable times. In Section 2, we shall introduce the concept of the limit cycles of such equations. We then establish, in Section 3, several criteria for the existence of the limit cycles of such systems. We shall apply a special impulsive integral function to obtain some necessary and su cient conditions for the existence of the limit cycles.