The headrest comprises a height-adjustable mounting (1) which is held in a projecting guide (3) and held in a support position for the head of the passenger. The mounting is slidable in the guide and can be stopped in several positions. There is a device which holds the headrest (S) in the support position in the event of a crash. The device may also put the headrest into the support position in the event of crash and retain it there. This is done in such a way that displacement of the mounting in both directions is blocked.