Abstract: Methane is converted into higher hydrocarbon products, and especially into ethane and ethylene, by oxidative coupling, by bringing a gaseous mixture containing methane and oxygen into contact at high temperature for a short contact time with a solid catalyst formed from lithium oxide, an alkaline earth metal oxide (preferably of magnesium) and a lanthanide oxide (preferably of neodymium or lanthanum), in which the lithium content is less than 0.20% by weight and the atomic ratio of the alkaline earth metal to the lanthanide varies from 0.8/1 to 8/1, said catalyst being obtained by:preparing a mixture of lithium, alkaline earth metal and lanthanide oxides in which the lithium content exceeds 1% by weight; andreducing the lithium content of the mixture to less than 0.20% by weight by high temperature thermal treatment conducted at least partly in an oxidizing atmosphere.