The present invention relates to a process for the manufacture of alkanes comprising a catalytic reaction resulting from contacting methane with at least one other starting alkane (I) in the presence of a metal compound (C) capable of catalysing a reaction for the splitting and/or recombination of a carbon-carbon bond and/or of a carbon-hydrogen bond and/or of a carbon-metal bond, which catalytic reaction results in the formation of at least one final alkane (II) having a number of carbon atoms equal to or greater than (2). In the process, the contacting operation is carried out under a methane partial pressure equal to or greater than 0.1 MPa, preferably in the range from 0.1 to 100 MPa. The metal compound (C) can be chosen from metal compounds supported on and dispersed over a solid support, metal compounds supported on and grafted to a solid support and non-supported metal compounds. Under these conditions, it was found that the yield of the catalytic reaction was improved, and that the catalytic stability and activity of the metal compound (C) over timer were greatly enhanced.