In order to achieve improved protection of the occupants of a motor vehicle, a side airbag is proposed which, when necessary, provides different hardnesses depending on the size of the vehicle occupant. The airbag includes at least one main chamber and at least one auxiliary chamber. The main chamber and auxiliary chamber are connected with each other via a connecting opening. Furthermore, an outflow opening is present from which gas can flow out of the airbag. The outflow opening is included in the auxiliary chamber. A closing element is provided which, when the auxiliary chamber meets an obstacle during or after expansion of the airbag, blocks or throttles the gas flow through the outflow opening.