Two procedures have been tested to produce concentrated methane hydrates in bulk, at medium to low pressure, avoiding the use of the high-pressure spray process. Both procedures have in common a first step of formation of the hydrate (30 % to 40 % mass fraction of water converted to hydrate) at (4 to 5) MPa and 275.16 K in a stirred reactor, starting from water and methane. Following this step, more hydrate was formed in the first procedure by cycling the temperature through the ice melting point. In the second procedure, pressure and temperature were cycled (after the first step) close to the hydrate stability boundary (about 4.3 MPa and 279.16 K). The second procedure is more effective, giving higher conversion yields, up to about 90 % water converted to hydrate.