Phase synchronization dynamics of Rssler oscillator in two coupled harmonic oscillators is discussed based on stability analysis of the coupled chaotic system. Different from the case of only one coupled periodic oscillator, in two o scillators one or the other harmonic oscillator will entrain alternately (or th ey will entrain exclusively). We find that depending on the stability of the system, the duration of the phase synchronization is affected by parameters of t he oscillator. The simulated results agree with our theoretic values within the range of error.