The dynamical behaviour of an automotive vehicle is analysed by use of a model with seven degrees of freedom for two load situations of the vehicle, loaded and unloaded, and for two different types of road, asphalt and paved. The vehicle velocity is varied between 5 and 30m/s. The passive linear suspension system is firstly optimized. Afterwards a system with passive elements in parallel with active elements with full and limited state feedback is optimized. To find the suspension elements characteristics it is used the stochastic optimal linear control theory through the minimization of the performance index whose constituent parts are: vehicle acceleration (comfort), suspension working space (structural limitation), road holding (safety) and control force.