A gas spring system of a vehicle includes a multi-chamber gas spring associated with each vehicle wheel. Each multi-chamber gas spring comprises a main chamber and at least one auxiliary chamber connectable to the main chamber, such that the spring rigidity of the multi-chamber gas springs can be changed. A control device determines a target axle rigidity as a function of a guide lateral acceleration and adjusts the target rigidity. The spring rigidity of the multi-chamber gas spring located on an inner side of the vehicle (relative to a curve traversed by the vehicle) is first changed. The spring rigidities of the multi-chamber gas springs of a vehicle axle are changed in stages in an alternating fashion.