To assure that the safety device is triggered at the right time in the event of a lateral collision of the vehicle with a curb, a first comparing device (1) compares a rotation rate (.omega.x) measured relative to the longitudinal axis of the vehicle, or a variable derived from this rotation rate, with a rotation rate threshold value. A second comparing device (2) compares an acceleration (ay), measured in the direction of the transverse axis of the vehicle, with a lateral acceleration threshold value. If both threshold comparing device (1, 2) simultaneously signal that their threshold values are being exceeded, a trigger signal (as1) for the safety device is output.