Due to the increased interest in magneto-hydrodynamic (MHD) based propulsion systems operating on the fundamental transposed-cycle (AJAX) the thermodynamic basis for selecting the cycle is reviewed. The fundamental transposed-cycle is defined by the turbine-burner-compressor configuration. The thermodynamic analysis of this configuration demonstrates that for a non-temperature limited engine the Bray to n Cycle will always yield higher values of specific thrust. When temperature limitations are imposed the transposed-cycle can yield higher specific thrust at the cost of increased specific fuel consumption.