The invention relates to an airbag system for a motor vehicle, comprising at least one inflatable airbag for protecting passengers. The aim of the invention is to influence, in different ways, the direction of expansion and depth of an airbag, irrespective of the cut of the airbag and irrespective of the course of the stitches of the airbag. According to the invention, at least one supplementary airbag is associated with a main airbag. Said supplementary airbag has a lower volume in order to increase the depth of deployment and/or to alter the direction of deployment of the main airbag.