In this paper we present a study of the switching kinetics of SrTiO3 based resistive switching memory devices. A pulse scheme is used to cycle the cells between the high resistive state (HRS) and the low resistive state (LRS) thereby monitoring the transient currents for a precise analysis of the SET and RESET transitions. By variation of the width and amplitude of the applied pulses the switching kinetics are studied between 10-8 and 104 s. Taking the pre-switching currents into account, a power dependency of the SET is found that emphasizes the importance of local Joule heating for the nonlinearity of the switching kinetics.