The invention relates to a heating or air-conditioning system for a motor vehicle, by which individual zones of the vehicle interior can be supplied with separately temperature-controlled air. An improved heating or air-conditioning system, which requires just a small amount of installation space, feeds differently temperature-controlled air to a plurality of air-conditioning zones. Despite the small amount of installation space, optimum mixing of cold air and warm air takes place in the heating or air-conditioning system, with the result that the air emerging from air-outlet openings in a respective air-conditioning zone have a constant temperature over the outlet cross section.