A process is described for the production of hydrocarbons with a high octane number starting from hydrocarbon cuts containing isobutene by means of selective dimerization with acid catalysts, characterized in that the dimerization reaction is carried out in a tubular reactor using a feeding containing isobutene in quantities of less than 20% by weight and with a molar ratio linear olefins/isobutene greater than 3, preferably operating at a reaction temperature ranging from 30 to 120.degree. C., at a pressure of less than 5 MPa and at feeding space velocities of less than 60 h.sup.-1.