This paper examined the quarter model of the vehicle suspension with dampers, represented by the hystereses models of Spencer type. The effectiveness of vibration reduction through the use of semi-active and passive systems with asymmetric damping force characteristics was compared. In case of semi-active dampers several different control algorithms of on-off type were considered. The impact of these algorithms on parameters associated with comfort and safety of the drive was analyzed. The results of the numerical simulations were presented in the form of graphs showing the values of performance indicators in the frequency domain.