The second law of thermodynamics is used to study the performance of single-stage and two-stage ammonia-water absorption refrigeration systems (ARSs) when some input design parameters are varied. The entropy generation of each component and the total entropy generation (<(S)over dot>(tot)) of all the system components as well as the coefficient of performance (COP) of the ARSs are calculated from the thermodynamic properties of the working fluids at various operating conditions. The results show that the two-stage system has a higher <(S)over dot>(tot) and COP, while the single-stage system has a lower <(S)over dot>(tot) and COP. This is a paradox since one would expect that an efficient thermal system should have a higher COP and lower <(S)over dot>(tot). This anomaly is explained with respect to the performance results for both single and two-stage systems. The trend in COP and <(S)over dot>(tot) with the change in heat exchangers effectiveness, absorbers temperatures and condenser and evaporator temperatures for both systems investigated conform with expectation, i.e. an increase in COP corresponds to a decrease in <(S)over dot>(tot). (C) 2003 Elsevier Ltd. All rights reserved.