Combustion within the channels of a wave rotor is examined as a means of obtaining pressure gain during heat addition in a gas turbine engine. Several modes of combustion are considered and the factors that determine the applicability of three modes are evaluated in detail: premixed autoignitionJdetonation, premixed defiagration, and non-premixed compression ignition. The last two will require strong turbulence for completion of combustion in a reasonable time in the wave rotor.The compressionJautoignition modes will require inlet temperatures in excess of 15000R for reliable ignition with most hydrocarbon fuels; otherwise, a supplementary ignition method must be provided. Examples of combustion mode selection are presented for two core engine applications that had been previously designed with equivalent 4-port wave rotor topping cycles using external combustion.