Systems and apparatuses are provided for controlling the speed of a driver's vehicle either in a first adaptive cruise control mode or a second travel or stop mode. In one embodiment, there is provided an apparatus comprising a speed control unit that executes a follow-up control based at least in part on a target inter-vehicle distance between the driver's vehicle and a preceding vehicle (i.e., another vehicle in front of the driver's vehicle). The speed control unit executes adaptive cruise control when the driver requests the follow-up control while traveling at a speed equal to or higher than a first predetermined vehicle speed. The control unit executes stop-or-travel control when the driver requests the follow-up control while traveling at a speed equal to or lower than another predetermined vehicle speed lower than the first predetermined vehicle speed.