Gas turbine engines with pulse detonation combustion show the superior performance in terms of specific work output and thermal efficiency when compared to the conventional gas turbine engines with isobaric combustion. But, a quasi-steady expansion of detonation products through the gas turbine results in an unsteady operation. Moreover, as the detonation products during quasi-steady expansion are initially at a very high temperature (over 2500 K), they cannot be expanded in the turbine as it is. To overcome the above difficulties associated with pulse detonation combustion in gas turbine engines, Air-Argon-Steam or organic fluid Combined Cycle (AASCC) is proposed in the present work. AASCC comprises two gas turbine cycles, viz. the Humphrey cycle with the air as the working fluid and the Brayton cycle with the argon as the working fluid and a steam turbine cycle, viz. the Rankine or organic Rankine cycle with the steam or organic substance as the working fluid. The temperature of the hot detonation products is reduced to Turbine Inlet Temperature (TIT) by exchanging heat energy between detonation products and compressed argon in a Detonation Products to Argon Heat Exchanger (DPAHE) and in turn, raising the temperature of the compressed argon to Argon Turbine Inlet Temperature (ATIT). The residual energy of both detonation products and argon after the expansion in the respective turbines is utilized to generate the steam or organic fluid vapor in the Heat Recovery Generators (HRGs) to operate a steam or organic fluid turbine. AASCC with pulse detonation combustion is analyzed based on quasi-steady state one dimensional formulation, and a computer code is developed in MATLAB to simulate the cycle performance at different compressor pressure ratios and TITs. C2H4/air is taken as the fuel-oxidizer. The performance of AASCC with pulse detonation combustion is compared with that of a conventional Air-Steam Combined Cycle (ASCC) with constant pressure combustion. It is found that the thermal efficiency of AASCC with pulse detonation combustion can go up to 44.5%–46.5% depending on the working fluid used in the bottoming Rankine cycle as against 37.8%–41.0% of ASCC at a TIT of 1400 K. The maximum specific work output of AASCC at a TIT of 1400 K is found to vary from 1143.0 to 1202.0 kJ/kg air as against to 335.0 to 364.0 kJ/kg air of ASCC.