Regimes of continuous spin detonation (CSD) with transverse detonation waves (TDWs) are obtained in a flow-type annular cylindrical combustor DK-500 for fuel-air mixtures (FAMs) with two compositions of the binary fuel CH4 + 8H2 and CH4 +4H2. Regimes of continuous multifront detonation (CMD) with colliding TDWs are obtained for the FAM with the CH4 + 2H2 binary fuel. These regimes are characterized by significant irregularity of the TDW structure and by a comparatively low TDW velocity. Specific impulses in continuous detonation are determined and analyzed for different compositions of the methane/hydrogen binary fuel. The maximum measured values of the specific impulse at the combustor exit are approximately 3800 s in CSD of CH4 + 8H2 and CH4 + 4H2, 3200 s in CMD of CH4 + 2H2, and 1600 s in combustion of CH4 + H2.