The four-phase coexistence curves for the structure-H hydrates of methylcyclohexane and cis-1,2-dimethylcyclohexane in the presence of methane are measured in the temperature range 274.09-288.29 K and pressure range 1.42-8.89 MPa. Very large pressure reductions from the pure methane hydrate are observed by forming structure-H hydrates. The present investigation on the trans-1,2-dimethylcyclohexane system reveals that the limit of the largest-cage occupancy for the structure-H hydrate is laid between the 1,2-dimethylcyclohexane stereo-isomers.