The design of the energy storage serving solar-powered LiBr–water absorption air-conditioning systems to meet 24-h a day operation is an important parameter that determines the performance of the system and optimizes its components. Introducing hybrid storage designs can improve system performance, reduce collector size, lower storage tank capacity, and hence make 24-h a day operating solar-powered LiBr–water absorption air-conditioning systems more feasible. Moreover, hybrid storage designs will ensure uninterrupted operation in case of maintenance for one of the storage tanks. This paper investigates four hybrid storage designs (heat and refrigerant storage, cold and refrigerant stfsorage, heat and cold storage, and heat, cold, and refrigerant storage) for a continuous operation (24 h a day) of solar-powered LiBr–water absorption air-conditioning. The study includes system description, features, and selection analysis for a constant cooling load of 5 kW in a typical family house in Dhahran City, Saudi Arabia. The results indicate that the hybrid cold and refrigerant storage system is the most suitable design for 24-h a day supply of the cooling effect. Copyright © 2016 John Wiley & Sons, Ltd.