Vehicle passive suspensions consist of two major elements generating force – spring and passive damper. Both possess non-linear characteristics, which are quite often taken into account in simulations; however, the friction forces inside the hydraulic damper and the damping force’s hysteresis are usually left out. The researchers in this paper present the results of examination of the influence of using complex damper models – with friction and hysteresis; and with linear and non-linear static characteristics – on the chosen dynamic responses of a suspension system for excitations in the typical exploitation frequency range. The results from the simulation tests of the simplified and advanced versions of the damper model – different transfer functions and their relation to the reference model’s transfer functions – are compared. The main conclusion is that friction and hysteresis add extra force to the already existing damping force, acting similar to damping increase for the base static characteristics. But this increase is not linear – it is bigger for smaller frequencies than for higher frequencies. The research shows the importance of including non-linear characteristics and proposed modules in modelling passive dampers.