A dynamic analysis of a free piston Vuilleumier cycle heat pump was performed using a time-stepping integration method to investigate transient characteristics under power controlling�DThe nonlinear relationship between displacement and force for pistons was taken into account for the motion of reciprocating components.The force for pistons is mainly caused by the pressure change of working gas varying With piston displacements�Gmoreover nonlinear viscous dissipative force due to the oscillating flow of working gas in heat exchangers and discontinuous damping force caused by solid friction at piston seals and rod seals are included.The displacements o fpistons and pressure changes in the Vuilleumier cycle heat pump were integrated by an ideal isothermal thermodynamic relationship�DIt was assumed that the flow friction was proportional to the kinematic pressure of working gas�Cand that the solid friction at the seals was due to the functions of the working gas pressure and the tension of seal sprlngs. In order to investlgate the transient characteristics of aproposed free piston Vuilleumier cycle heat pump machine when hot-side working gas temperatures and alternate force were changed�Csome calculations were performed and discussed.These calculation results make clear transient characteristics at starting and power controlling�DIt was further found that only a small amount of starter power is required at particular conditions.During controlling�Cthe machine becomes unstable when there is a relatively large reduction in cooling or heating power�DTherefore�Can auxiliary device is additionally needed to obtain stable operation�Csuch as a linear motor�D