This work is devoted to the study of the entropy generated and the exergy destroyed in the lithium bromide absorption thermal compressors of single and multiple effects, driven by the heat of the exhaust gases of an engine, when the absorption hear is directly transferred either to water or to air. Air-cooled systems work with temperature and pressure gradients higher than those cooled by water. The absorption temperature in air-cooled systems can reach and even exceed 50 degreesC. Under these conditions, boiling temperature within the high desorber of the double and triple effect systems can exceed 200 and 300 degreesC, respectively. Maximum pressures reach values of 1.7 and 15 bar, respectively. The thermal compressor cooled by air generates more entropy and destroys more exergy than the one cooled by water. The triple-effect thermal compressor destroys less exergy than the one of double effect and the latter destroys less exergy than the one of single effect. The lithium bromide thermal compressor of single effect cooled by air is not feasible when working with absorption temperatures around 50 degreesC. The one of double effect is feasible since the high-pressure desorber can work at higher temperatures. Under these conditions, the solution cycle described within the high-pressure desorber remains out of the zone of crystals formation, and offers the possibility of producing more refrigerant than the one of single effect. Also, in the double-effect compressor less entropy is generated, and therefore less exergy is destroyed than in the single effect. The triple-effect compressor cooled by air offers the possibility of producing more refrigerant than the one of double effect, but at higher expenses of temperatures and boiling pressures of the solution. This creates corrosion and control problems, which do not have an easy solution yet. Less exergy destruction does not compensate for the increase of these problems. In any case, the compression process of the cooling steam occurs with entropy reduction. Copyright (C) 2000 John Wiley & Sons, Ltd.