The present invention provides an adsorbent for adsorption heat pump and humidity-control air conditioner, which is capable of adsorbing an adsorbate therein and desorbing the adsorbate therefrom in a narrow relative vapor pressure range, and can be regenerated (desorption) at a low temperature. Also, the present invention provides an adsorption heat pump and humidity-control air conditioner using the adsorbent which can be effectively operated even by a low-temperature heat source, as well as methods of operating the adsorption heat pump and humidity-control air conditioner by effectively utilizing low-temperature exhaust heat. The absorbent of the present invention comprises zeolite containing (i) aluminum, (ii) phosphorus and (iii) iron and/or gallium in a skeletal structure thereof, which is substantially free from change in structure upon subjecting the adsorbent to adsorption and desorption of water vapor, and has an operable relative vapor pressure range in which a change in amount of water adsorption of the absorbent when changing the relative vapor pressure by 0.1 in a relative vapor pressure range of from 0.1 to 0.25 in a water vapor adsorption isotherm measured at a temperature of 25° C., is not less than 0.12 g/g.