In this paper we consider optimal designs of partially step-stress life testing which is deviced for k-component series systems with the considerably long life time. Test items are first run simultaneously at use condition for a specified time, and the surviving items are then run at accelerated condition until a predetermined censoring time. The optimal criterion for the change time to accelerated condition is to minimized either the generalized asymptotic variance of maximum likelihood estimators of the hazard rates at use condition and the acceleration factors or the asymptotic variance of the maximum likelihood estimators of the acceleration factors.