This study investigates the performance and efficiency of closed-loop oxy-hydrogen Brayton power cycles through numerical modelling and simulation. Coupled with storage hydrogen and oxygen produced by a water-electrolysis system, these cycles have the potential to produce flexible electrical power at high thermal efficiency whilst producing zero exhaust gas emissions. The efficiency and power output of the cycles are investigated using a thermodynamic model. A standard Argon Power Cycle (APC) fuelled by hydrogen is explored which yields an efficiency of 19% under typical operating conditions. To improve the performance, the cycle is modified by including an intercooler, reheater and regenerator, which has the potential to increase the efficiency to 64% when operating under the same conditions. In addition, the potential use of helium and air as the working fluid is explored, as well as a methane fuelled cycle. It is found that the hydrogen–helium cycle is more efficient over all pressure ratios but the most expensive to operate.