Throughout the years many control strategies for adjustable dampers have been proposed, designed to boost the performance characteristics of a vehicle in area of comfort and safety. Those control strategies have been tested many times using simulation models of vehicles in which tested were such strategies as Skyhook, Acceleration Driven Damping or Power Driven Damping. Those tests however were carried out using simplified damper models with simple two-linear, symmetric characteristics. The researchers in this article examine the influence of using more complex damper models, with friction, hysteresis and time-delay of state-switching implemented, on the chosen dynamic responses of a suspension system for excitations in the typical exploitation frequency range. Model was developed on the base of other researchers proposal and own experimental tests of real adjustable shock absorber tests. The results from the test were processed to obtain transmissibility functions which were then analyzed and compared with those found in other researches and with the simplified version of the advanced model.