Lowering the exergy content of heat required for heating purposes decreases the primary energy consumption. District heating systems are often an important link between facilities that generate heat with low exergy content and consumers. Exergetic efficiency of heat distribution is an important performance criterion in heat supply to consumers. It can serve as a criterion for optimization, towards a more sustainable distribution-network design and operation. This paper presents a methodology for an exergy-based distribution-network analysis in a district heating system. Criteria for performance evaluations are defined. They can be used to evaluate heat supply to different points in the network, or individual system components. A case study is performed on an existing district heating system. Energetic and exergetic efficiencies of supply lines are analyzed. Exergy destructions and exergy losses are studied. Large differences in efficiency of heat supply to different points in the network are discovered. Over-dimensioned parameters of the distribution network are investigated.