The kinetic dependences of the accumulation of carbon during pyrolysis of CH4 mixed with H2 on an Mo-Co/MgO catalyst with the atomic ratio Mo: Co: Mg = 3: 1: 76 at atmospheric pressure, temperature 900°C, and various CH4 and H2 partial pressures were determined by direct thermogravimetric measurements in combination with electron microscopic examination. The main solid pyrolysis products were found to be carbon nanotubes with two to five walls. The outside diameter of nanotubes changed from -3 to 9 nm. A kinetic model of the accumulation of carbon was suggested. The model took into account the formation of two products, nanotubes and carbon deposited on their surface, process reversibility, and catalyst deactivation by nanotubes formed.