The use of ideal absorption cycles with external heat transfer irreversibilities to obtain the performance limits of solar-operated absorptions systems is considered in this paper. The absorption machine is represented by the three-heat-reservoir ideal cycle and it is supplied with energy from a solar collector-storage system. Analytical expressions are obtained for the coefficient of performance, the cooling capacity, the entropy production and the second-law efficiency of the system. The results obtained for cycles with external heat transfer irreversibilities and for fully reversible cycles are compared with those obtained by detailed simulation of the absorption machine. Externally irreversible cycles are found to give realistic upper limits to the cooling capacity and the coefficient of performance of solar-powered absorption cooling systems.