A self-consistent model has been developed to simulate the kinetics of alternate oscillation of self-terminating and recombination lasers in univalent ions of strontium excited by high-repetition-rate pulsed discharge. Photoelectric pulse waveforms predicted by the model are in good agreement with the experimental measurement. Temporal behaviors of long-life particles， the upper and the lower level poplulations and the electron temperature in He-Sr discharge plasma are given by the model. The emission process of the two laser alternate oscillation， the characteristic of the laser pulse width and the population inversion mechanics are also analyzed. It is presumed whether the electron temperature can rise up quickly in the early discharge and fall down rapidly during the discharge afterglow is the key to realize the alternate oscillation of self-terminating and recombination lasers in univalent ions of strontium in experiment.