The invention concerns a process for isomerising a feed containing essentially hydrocarbons, preferably paraffins preferably containing 5 and/or 6 carbon atoms per molecule, in which said feed is treated in a distillation zone comprising an exhausting zone and a rectification zone associated with an isomerisation reaction zone, in the presence of an isomerisation catalyst and a gas stream containing hydrogen, characterized in that the reaction zone is at least partially internal to the distillation zone, and wherein the hydrogen-containing gas is fed by a dedicated gas distributor to the bottom of at least one catalytic bed within the isomerization reaction zone.