A preliminary study of the combined gas-turbine vapour-turbine engine and a blade-to-blade design method for high Mach number axial flow turbines are presented. Cycle calculations were carried out and vapour turbines were examined to determine the probable plant performance and to provide an indication of the vapour turbine design problems using a number of different vapour cycle working fluids. It was shown that the combined engine could have an efficiency slightly higher than a regenerative gas-turbine and specific out-put 30% higher than a simple gas turbine. Vapour turbines using Refrigerant fluids are shown to be comparatively small and to present the design problems of high flare and high Mach number. Refrigerant 21 appears to be the best working fluid. A blade-to-blade design tool for analysing the subsonic, transonic and supersonic flows in axial turbines was formulated using the streamline curvature method. The convergence of the numerical procedure was analysed and a satisfactory method developed which produced convergence for a digital computer and computed results were compared with results from experiment and other theory. Comparisons for turbine type cascades up to Mach 1.0 show a satisfactory agreement and techniques introduced give improved leading edge results and allow a good approximation to the trailing edge Kutta-Joukowski condition to be applied. Predictions for convergent divergent supersonic wind tunnel type nozzles agree closely with experiment and with other methods. Numerical difficulties are found to be more acute for subsonic-supersonic turbine cascades and experimental agreement is acceptable only up to low supersonic Mach numbers.