To provide an absorption cooling and heating machine that can perform stable, efficient and economical drive operation by avoiding a generation phenomenon of the on/off-operation of drive as much as possible, and its operation control method.

An absorption refrigerator includes: a high-temperature recovery machine 1 and a low temperature recovery machine 2; a condenser 3; an evaporator 4; an absorber 5; and a low temperature heat exchanger 6 and a high-temperature heat exchanger 7 which are connected in piping. The absorption refrigerator which is driven by burner-type combustion devices 41 to 46 arranged at the recovery machine controls the combustion devices 41 to 46 so as to avoid the repetition of on/off-operations by performing the minimum drive mode which is drive at the lowest combustion level while combustion is stabilized when a cold/warm water outlet temperature of cold/warm water piping 22 reaches a prescribed trigger temperature.