Vehicle occupant restraint system

The system has a front air bag (3), a separate lateral air bag (6) that extends as far as the front air bag when inflated, a controller for activating the air bags that is programmed so that it activates both air bags in the event of a frontal impact and/or a laterally offset frontal impact and/or an oblique frontal impact or alternatively in the event of a laterally offset frontal impact and/or an oblique frontal impact.