There are heat losses during the cycle of real engine that are neglected in ideal air-standard analysis. In this paper, the effect of heat transfer on the net output work is shown and thermal efficiency of the air-standard Atkinson and the Dual combustion cycles are analyzed. Comparison of performances of the air-standard Atkinson and the Dual combustion cycles with heat transfer considerations are also discussed. We assumed that the compression and power processes are adiabatic and reversible and any convective, conductive and radiative heat transfer to cylinder wall during the heat rejection process may be ignored. The heat loss through the cylinder wall is assumed to occur only during combustion and is further assumed to be proportional to average temperature of both the working fluid and cylinder wall. The results show that the net work output versus efficiency and the maximum net work output and corresponding efficiency bounds are influenced by the magnitude of heat transfer. The results are of importance to provide guidance for the performance evaluation of practical engines.