A process for isomerising a feed comprising normal paraffins containing 5 to 8 carbon atoms per molecule as a major portion in the presence of hydrogen, characterized in that the sum of the amounts of normal paraffins containing 7 and 8 carbon atoms per molecule contained in the feed is in the range 2% to 90% by weight with respect to the feed, and in that said feed is treated in at least one reaction zone, containing at least one catalyst in a fixed bed, said catalyst comprising a support, at least one halogen and at least one group VIII metal, the reaction being carried out at a temperature in the range 30 to 150° C.