On the basis of an endoreversible absorption heat-pump cycle, a generalized irreversible four-heat-reservoir absorption heat-pump cycle model is established by taking account of the heat resistances, heat leak and irreversibilities due to the internal dissipation of the working substance. The heat transfer between the heat reservoir and the working substance is assumed to obey the linear (Newtonian) heat-transfer law, and the overall heat-transfer surface area of the four heat-exchangers is assumed to be constant. The fundamental optimal relations between the coefficient of performance (COP) and the heating load, the maximum COP and the corresponding heating-load, the maximum heating-load and the corresponding COP, as well as the optimal temperatures of the working substance and the optimal heat-transfer surface areas of the four heat-exchangers are derived by using finite-time thermodynamics. Moreover, the effects of the cycle parameters on the characteristics of the cycle are studied by numerical examples. (c) 2004 Elsevier Ltd. All rights reserved.