Four approaches to the diagnosis of malfunctions in energy systems are presented and applied to the same test case plant. The paper is part of a project, started in 2001 and named thermoeconomic approach to the diagnosis of energy utility systems (TADEUS), aimed at integrating various experiences accumulated by a group of researchers operating in the thermoeconomic diagnostics, a field of research started by Antonio Valero and co-workers in 1990 and then followed by various people all over the world. It is shown how, starting from the same basic set of ideas, researchers developed different approaches, each one having peculiar characteristics that are, however, complementary to each other. (C) 2006 Published by Elsevier Ltd.