The present study investigates dynamic response of vehicle models, subjected to road excitation. In these models, a semi-active control strategy is applied on the suspension dampers, which is based on a switch of their damping coefficient between different values, so that the resulting system approximates the performance of a vehicle involving sky-hook damping. An alternative control strategy is also applied, which is passive and is based on selecting a different damping ratio when the wheel velocity relative to the car body is positive or negative. Both of these control strategies lead to oscillator models with parameter discontinuities. Similar terms are also introduced into the equations of motion by considering wheel hop phenomena, where a vehicle wheel leaves the ground temporarily. First, simple quarter-car models are examined but the analysis is also applied to more complicated models. For these models, their dimensions are reduced substantially by applying a component mode synthesis approach. Subsequently, this allows the efficient application of appropriate methodologies for predicting response spectra of the nonlinear models to periodic road excitation. Finally, results obtained by direct integration of the equations of motion are also presented for transient road excitation. In all cases, the results are compared to those obtained for vehicles with suspensions including passive shock absorbers. Moreover, special consideration is given to cases where wheel hop is possible to occur.