A local stability analysis of an endoreversible Curzon-Ahborn-Novikov (CAN) engine, working in a maximum-power-like regime, is presented. The CAN engine in the present work consists of a Carnot engine that exchanges heat with the heat reservoirs T 1 and T 2 (T 1 > T 2 ) through a couple of thermal conductors, both having the same conductance (α). In addition, the working fluid has the same heat capacity (C) in the two isothermal branches of the cycle. From the local stability analysis we conclude that the CAN engine is stable for every value of α, C and τ = T 2 /T 1 ; that after a perturbation the system state exponentially decays to the steady state with either of two different relaxation times; that both relaxation times are proportional to C/α; and that only one of them depends on τ , being a monotonically decreasing function of τ . Finally, when comparing with the system steady-state energetic properties, we find that as τ increases, the system stability is improved, while the system power and efficiency decrease; this suggests a compromise between the stability and energetic properties, driven by τ .