Regimes of continuous detonation of methane/hydrogen-air mixtures in spin and opposing transverse detonation waves are obtained for the first time in a flow-type annular cylindrical combustor 503 mm in diameter. A two-component (methane/hydrogen) fuel with the H-2 mass fractions of 1/9 to 1/2 in the range of specific flow rates of the mixture from 64 to 1310 kg/(s center dot m(2)) and the fuel-to-air equivalence ratio I center dot = 0.78-1.56 is considered. In methane/hydrogen-air mixtures with two compositions of the fuel (CH4 + 8H(2) and CH4 + 4H(2)), one-wave and two-wave regimes of continuous spin detonation are obtained; the frequency of rotation of transverse detonation waves is 0.56-1.66 kHz at I center dot = 0.78-1.02. For the fuel compositions CH4 + 2H(2) and CH4 + 1.5H2, continuous multifront detonation with two opposing transverse detonation waves rotating with the frequency of 0.86-1.34 kHz at I center dot = 1.0-1.23 is obtained. For the CH4 + H-2 + air mixture, both combustion in the chamber and continuous spin detonation outside the combustor with transverse detonation waves rotating with the frequency of 1.01-1.1 kHz are observed. The lean limits of continuous detonation are obtained in terms of the specific flow rate of the mixture: 64, 100, 200, and 790 kg/(s center dot m(2)) for the fuel compositions CH4 + 8H(2), CH4 + 4H(2), CH4 + 2H(2), and CH4 + 1.5H(2), respectively, for the mass fraction of hydrogen in the methane/hydrogen fuel of ae0.16. Violation of regularity of the continuous detonation wave structure and the wave velocity with a decrease in the fraction of hydrogen in the two-component fuel is detected.