Higher hydrocarbons are produced from methane by reacting the methane at elevated temperature, suitably in the range from 600 to 800°C, with an oxygen-containing gas having a ratio of methane to oxygen of greater than the stoichiometric ratio for complete combustion in the presence as catalyst of a lithium-doped material which under the reaction conditions is a physically base-stable, non-melting, oxygen-stable compound of an element of Groups III to VIII of the Periodic Table of the Elements including the rare earth elements.