PURPOSE: To provide a car running control device which presents adjustability for the transition acceleration from the followup running to the constant speed running without forcing the driver any particular manipulation and which enables smooth running to well suit the driving feeling.

CONSTITUTION: Signals from a radar device 10 and a car speed sensor 12 are fed to an electronic control device ECU 16. The ECU 16 is also supplied with signals from a setting SW 13, into which the set car speed for constant speed running is fed, and a SW 14 to make Hi/Lo changeover of the headlights. The ECU 16 controls a throttle actuator 18 or brake actuator 20 to maintain the safe inter-car distance so that the car makes followup running after the foregoing car, and in case no car foregoing is sensed by the radar device 10, makes constant speed running control. When transition is made from the followup running to the constant speed running, the acceleration at transition is adjusted by the Hi/Lo changeover SW 14 for headlights.