The effect of the rotor system with nonlinear flexible supports passing through the resonance area is studied,when the system is at the transient process of starting or breaking.The stiffness with hard nonlinear feature can cause the critical speed and the maximum amplitude of the transient processes increase.It is no benefit for the rotor system to pass through the resonance area rapidly.The effect of the transient acceleration on the maximum amplitude of the transient processes has also been researched in the paper.At last the rotor system with slow changing stiffness has been analyzed.