This paper studies the nonstationary vibration of a rotating shaft on flexible supports in passing through the critical speed. In particular the interaction or the coupling effect caused by near critical speeds in continuous passing through 1st and 2nd critical speeds has been studied. For the case of a rotor system on damped flexible supports, its approximate equation in transition through the critical speed has been derived by the asymptotic method as in the former report. Moreover, observing nonstationary maximum amplitudes, the analytical results have been considered. The experiments support the analysis.