Vehicle control apparatus, vehicle control method, and vehicle following running system

According to one aspect of the present invention, a vehicle control apparatus mounted on a lead vehicle sets a smaller value of a first acceleration limit value determined based on specifications regarding running of a first following vehicle and a basic acceleration limit value determined based on specifications regarding running of the lead vehicle as a set acceleration limit value of the lead vehicle, and outputs an acceleration instruction for controlling a braking apparatus or a driving apparatus after limiting it according to the set acceleration limit value.