Abstract: A process for processing a feedstock comprising a major amount of olefinic hydrocarbons having 4 carbon atoms per molecule, including isobutene as well as but-1-ene and but-2-enes, wherein the process comprises processing said feedstock in a distillation zone associated with a hydroisomerization reaction zone located at least partly external to the distillation zone, said processing comprising drawing at the height of a draw-off level of the distillation zone at least part of the liquid flowing in the distillation zone, passing said liquid into the external hydroisomerization reaction zone to form a hydroisomerized effluent, and reintroducing at least part of the effluent from said reaction zone reintroduced into the distillation zone at one or more reintroduction level(s), so as to ensure the continuity of the distillation.