Numerical simulations with detailed chemistry are conducted for two-dimensional rotating detonative combustion with separate injection of fuel and oxidant. The influences of the fuel and oxidant compositions on combustion mode and detonation wave multiplicity are studied. It is found that in the parts of the flow beyond the fuel refill zone, there are two distinct, highly inhomogeneous zones with fuel-rich and fuel-lean compositions, respectively. Both detonative and deflagrative regimes are observed and proceed mostly under a premixed combustion mode with the deflagration confined mostly to the fuel-lean zone. The results from our simulations show that limited H-2 is detonated or deflagrated close to stoichiometric conditions and more than 70% of H-2 is detonated or deflagrated under fuel-lean conditions. Over 70% of the detonated H-2 is consumed in a premixed combustion mode. Our analysis also suggests that the detonation fraction increases with increased inlet pressure, decreased inlet temperature or increased injection orifice number. Additionally, the range of mixture fraction over which the composition is detonable is narrower than the range for deflagration. The number of detonation waves increases with increased oxygen mass fraction in the oxidant stream, with the additional waves being formed by mutual enhancement of an explosive hot spot and a travelling shock wave. Stabilization of the multiple waves follows a chaotic period involving both co-rotating and counter-rotating waves. Furthermore, the deficit of the detonation speed relative to the ideal Chapman-Jouguet value increases with the number of waves but also decreases monotonically with the level of reactant mixing. The reactant mixing effects along the detonation wave height are further discussed through quantifying the statistics of height-wise mixture fraction, heat release rate and OH mass fraction. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.