In the present study, an optimal performance analysis based on maximum power (MP) and maximum efficiency criterion including internal irreversibility for steady state operation has been performed for the air standard Dual cycle. It is shown that the effect of internal irreversibility such as friction on MP may be characterised by the cycle irreversibility parameter representing the ratios of entropy differences for the cycle. The presence of this parameter in the equations for the MP and the corresponding efficiency shows that an engine with internal irreversibility delivers less power and has a lower efficiency than a reversible engine. The effect of the design parameters such as pressure ratio, cut off ratio and extreme temperature ratio of the cycles has also been investigated under the MP and maximum efficiency conditions on the basis of having the internal irreversibility. Also in the present study, performance analysis has been extended to the Otto and Diesel cycles which may be considered as special cases of the Dual cycle.