The wave rotor is a promising means of pressure-gain for gas turbine engines. This paper examines novel wave rotor topping cycles which incorporate low-NOx combustion strategies. This approach combines two-stage ‘rich-quench-lean’ (RQL) combustion with intermediate expansion in the wave rotor to extract energy and reduce the peak stoichiometric temperature substantially. The thermodynamic cycle is a type of reheat cycle, with the rich-zone air undergoing a high pressure stage. Rich-stage combustion could occur external to or within the wave rotor. An approximate analytical design method and CFD/combustion codes are used to develop and simulate wave rotor flow cycles. Engine cycles designed with a bypass turbine and external combustion demonstrate a performance enhancement equivalent to a 200–400°R (110–220°K) increase in turbine inlet temperature. The stoichiometric combustion temperature is reduced by 300–450°R (170–250°K) relative to an equivalent simple cycle, implying substantially reduced NOx formation.