The irreversibilities (exergy destruction) within a component of an energy conversion system can be represented by two parts. The first part depends on the inefficiencies of the considered component while the second part depends on the system structure and,the inefficiencies of the other components of the overall system. Thus, the exergy destruction occurring within a component can be split into two parts: (a) endogenous exergy destruction due exclusively to the performance of the component being considered and (b) exogenous exergy destruction caused also by the inefficiencies within the remaining components of the overall system. The paper discusses four different approaches developed by the authors for calculating the endogenous part of exergy destruction as well as the approach based on the structural theory. The advantages, disadvantages and restrictions for applications associated with each approach are presented. It is concluded that all approaches developed by the authors lead to comparable and acceptable results, whereas the structural theory approach should not be used for calculating the endogenous part of exergy destruction because it delivers unacceptable results. Splitting the exergy destruction into endogenous and exogenous parts improves our understanding of the interactions among system components and provides very useful information for improving an exergy conversion system, particularly when this concept is combined with the concept of avoidable and unavoidable exergy destruction. (C) 2008 Elsevier Ltd. All rights reserved.