Efficiency improvements are very important in all research and technology. Detonation engines are high technology devices. In the last decades they attracted attention by many researchers. However, detonation engines for cogeneration are not researched efficiently. This article is about the detonation engines cogeneration cycles which analysed by using 1. and 2. law of thermodynamics and exergy analyses methods by the authors. The exergetic performance analyses, their advantage and disadvantages of the ZND-HRSG detonation engine cogeneration cycles were obtained. The exergetic performance analyses were done for various excess air rates to obtain the variations of the combustion exit pressures and temperatures, exergy efficiencies, electric heat rates, SFC and other parameters of their performance. Also, an optimization analysis was done for the ZND-HRSG by searching the optimum values for different excess air rates. The results showed that, the ZND-HRSG cycle have the optimum values of the performance at 1.6-1.8 of the excess air rates.