Air conditioning system for multi-zone air conditioning of a motor vehicle interior comprising a casing with a mixing chamber and several zone outlets outgoing from mixing chamber, in which an evaporator and at least one heat exchanger are disposed such that main air flow from evaporator through at least one heat exchanger into zone outlets is linear and at least two bypass channels, each comprising a louver, in order to circumvent at least one heat exchanger connect a region downstream of evaporator and a region downstream of at least one heat exchanger, wherein the first bypass channel, as a mixing bypass channel, opens out into mixing chamber and the second bypass channel, as a stratification bypass channel, opens out into a zone outlet.