In this work, the effect of different injector geometries and different outlet restrictions on the operating modes of a hydrogen-air Rotating Detonation Combustor (RDC) is investigated. The different operating modes are identified based on pressure measurements in the combustor annulus and the reactant supply, combined with high-speed video from the aft end of the combustor. The pressure frequency spectra are analyzed to determine the global operating mode in terms of number, direction, and speed of waves. The results explore the ability of the RDC to establish rotating, counter-rotating, and longitudinal waves, as well as their superpositions. A good agreement between longitudinal modes and the acoustic resonance frequencies of the RDC annulus was found. Overall, operation was found to be highly injector and outlet restriction dependent. Adding an outlet restriction helped to suppress counter-rotating waves, which is a prerequisite to stabilize single detonation waves. However, it was also shown to prompt high frequency pulsed operation. Apart from the total reactant supply pressure, the relative strength of the injectors was identified as a key factor for stable RDC operation. Pressure feedback into the reactant supply was observed to be dependent on the reactant supply pressure and the RDC operating mode. The study further revealed the presence of transverse resonance modes in the fuel plenum, however these oscillations were weak relative to the injector pressures and do not appear to influence the combustion. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.