Abstract: A process and apparatus for the thermal conversion of methane into hydrocarbons of higher molecular weight, comprising a reactor (1) of elongate form, connected on the one hand, at a first end, to means (5) for supplying gaseous mixture containing methane (process gas) and on the other, at the opposite end, to discharge means (10), the said reactor comprising on a first part (the first end side) a plurality of elements disposed in at least two layers, substantially parallel inter se and substantially perpendicular to the axis of the reactor, at least one of these layers comprising a series of sheaths (4) inside which there are electric heating means (3) which thus form a layer of heating elements, the said elements being disposed in such a way as to define between them and/or between the layers which they form and/or between them and the walls of the spaces or passages for the circulation of gaseous mixtures and/or effluents, the said heating means and the said sheaths being adapted to heat the said passages