A headway distance maintenance supporting system may include a running controller for performing constant headway distance control, a deceleration controller for performing deceleration support control, a transitional state detector for detecting transitional states of said given vehicle based on the running environment of said given vehicle or the operations performed by the driver. The system controller is configured such that when said transitional state detector detects that the transitional state of said given vehicle is a prescribed transitional state, said running controller is controlled such that said constant headway distance control is released, and said deceleration controller is controlled such that said deceleration support control can be performed.