An airbag assembly for a motor vehicle is disclosed having an airbag 110 that is inflated by an inflator when the airbag 110 is deployed in accordance with a control signal from an electronic controller. The airbag 110 has a main chamber 114 and at least one subsidiary chamber 116 fluidly connected to the main chamber 114 by a transfer vent 117. The main and subsidiary chambers 114 and 116 are vented to atmosphere by respective vents 115, 118 and the pressure in the subsidiary chamber 116 is arranged to be equal to or lower than the pressure in the main chamber 114. The subsidiary chamber 116 is produced in a simple manner by forming a depression in the main chamber 114 using a tether 124 and covering the depression so formed with a cover 125.