An air conditioning system and a method for operating the air conditioning system, in which a plurality of compressors are simultaneously or selectively operated, based on the difference between a room temperature and a desired temperature generated during a waiting time for re-operation of the compressors. The room temperature varying during the waiting time for the re-operation of the compressors maintained at a stopped state is sensed to determine whether or not an increase in cooling load occurs. Based on the amount of the cooling load, it is determined whether the compressors have to operate simultaneously or selectively. That is, the refrigerant compression capacity of the air conditioning system is determined by reflecting the cooling load caused by a variation in room temperature occurring during the waiting time for re-operation taken until any compressor maintained in a stopped state is re-operated. Accordingly, it is possible to more stably control the room temperature, and to achieve an improvement in the comfortableness of the room atmosphere.