The problem of increasing the thermodynamic efficiency of power plants can be solved only by using a complex approach using methods based on modern methods of exergy analysis in combination with methods of heat transfer theory, theory of linear systems, structural-variant methods, multi-level optimization methods, etc. The analysis of the possibility of applying the discrete-modular principle and the corresponding complex method for analyzing the efficiency of the exhaust gases heat-recovery exchanger of a cogeneration unit heat engine is performed in the paper. The aim of the work is to analyze the localization of exergy losses, their differentiation, and the establishment of the relative contribution of various types of losses to the general exergy losses in the exhaust gases heat-recovery exchanger of a cogeneration unit heat engine. The structural features of the heat-recovery exchanger and the exergy properties that reflect the essence of exergy methods: universality and additivity, made it possible to use the discrete-modular principle and a complex method based on exergy-dissipative functions for efficiency analysis. The advantage of this method is the ability to analyze the localization of exergy losses in separate modules of the heat-recovery exchanger and to differentiate the exergy losses associated with nonequilibrium heat transfer between the heat-transfer agents and the wall, heat conduction and the movement of heat-transfer agents. Using the chosen complex method, the analysis of the localization of exergy losses in the heat-recovery exchanger was carried out and the exergy-dissipative functions of each of the eight modules of the heat-recovery exchanger were calculated. Differentiation of exergy losses was carried out and the relative contribution of exergy losses associated with the processes of heat transfer from flue gases to the wall, from wall to water, in heat conduction processes, as well as exergy losses associated with the movement of heat-transfer agents, in the general exergy losses was analyzed. To determine the exergy losses due to nonequilibrium heat transfer between the heat-transfer agents and the motion of the heat-transfer agents, the differential exergy equations, the equations for the heat flow densities between the heat-transfer agents and the wall, the equation for the heat flow density due to heat conduction through the wall and the equations of motion are used. It has been established that the localization of maximum exergy losses in all modules of the heat-recovery exchanger is associated with losses due to heat transfer from flue gases to the wall.