Optimal configuration of a class of endoreversible heat-engines, with fixed duration and subject to the radiative heat-transfer law q proportional to Delta(T-4), has been determined. The optimal cycle that maximizes the power output of the engine has been obtained using optimal-control theory, and the differential equations are solved by a Taylor-series expansion. It is shown that the optimal cycle has six branches, including two isothermal branches and four maximum-power branches, without adiabatic branches. The interval of each branch has been obtained, as well as the solutions of the temperatures of the heat reservoirs and working fluid. A numerical example is given. The results are compared with those obtained using the Newton's heat-transfer law for maximum power-output and those using a linear phenomenological heat-transfer law for maximum power output. (c) 2006 Elsevier Ltd. All rights reserved.