The invention relates to a speed control for motor vehicles, comprising a sensor device for measuring operational parameters of the vehicle and for measuring the distance to a target object in front of the vehicle, a control device for controlling speed or accelerating the vehicle in accordance with the measured operational parameters and distance data, a switch-off command input device (S2) for switching off the control and a switch-off function for switching off (S4) the control in accordance with other commands (S6, S7, S8, S9) of the driver. The control is provided with a stop function for automatically decelerating the vehicle to a standstill, the switch-off command input device (S2) being ineffective when the stop function is active (S3) and the vehicle is at a standstill (S5).