This study is concerned with the performance analysis and comparison of air standard Diesel and Diesel-Atkinson cycles with heat-transfer loss, friction like term loss and variable specific-heat ratio of the working fluid based on finite-time thermodynamics. Also numerical examples are detailed to show the relations between the output power and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between the output power and the thermal efficiency of both cycles. Furthermore, the effects of variable specific-heat ratio of the working fluid, heat transfer and the friction-like term loss on the performance of both irreversible cycles are analyzed. Comparison of the performance of cycles shows that the heat efficiency and the output power of an air standard Diesel-Atkinson are higher than the Diesel ones and the points of maximum output power and thermal efficiency of Diesel-Atkinson cycle occur at the lower compression ratio. Reduction of Noxis another advantage of Diesel-Atkinson cycle. The results obtained in this paper provide guidance for the design of Diesel and Diesel-Atkinson engines.