A process is provided for the production of linear saturated alkanes from one or more primary alcohols, wherein the carbon chain of the one or more primary alcohols has one carbon atom more than the alkane, including conducting reductive dehydroxymethylation of one or more primary fatty alcohols containing 8 to 24 carbon atoms, at a temperature ranging from 100 to 300° C. and pressures from 1 to 250 bar in the presence of hydrogen and a catalyst, and removing water formed during the reaction.