Computer simulations of the kinetics of the methane oxidative coupling in a plug flow-type reactor at 723-873 K and 0.2-0.6 MPa have been performed. It is shown that the C-2 hydrocarbons and carbon oxides are predominantly formed by the parallel reaction pathways. The heterogeneous catalyst that enables to accelerate the methyl radical formation as well as to decompose the most stable reaction intermediates (CH2O, H2O2 and HO2) can considerably shift the selectivity and yield of the homogeneous branching chain reaction towards ethane and ethylene formation. The certain accordance between experimental and calculated data indicates this supposed kinetic model to reflect some important features of the heterogeneous-homogeneous methane oxidative coupling under explored reaction conditions.