Abstract: Local stability of an irreversible Carnot heat engine at the maximum power output and the optimum ecological function has been studied based on the optimal performance parameters of the heat engine based on the Newton transfer heat law and using the local stability analysis. Expressions of relaxation time describing stability are derived. Relationship between relaxation time and heat-transfer coefficient ratio a/b, heat capacity C, total heat exchange area F, temperatures of heat reservoirs TH and TL, and heat leak are found. The characteristics of local stability at two steady states are compared. It is concluded that the optimal performance and local stability of the system should be considered simultaneously both in design and application.