The invention relates to the preparation of oligomers starting from linear alpha-olefins and to the subsequent hydrogenation thereof to saturated oligomers products, and more particularly to the catalyst system used in the oligomer preparation reaction, the catalyst system consisting of a first component selected amongst the halogenated organo-metal aluminium components, and a second component capable of reacting with the first one and chosen amongst halogens or interhalogenic compounds and metal halides; thus higher yields of oligomers, as well as an easier performance and a control of the reaction are achieved. In turn the hydrogenation step is carried out in the presence of a known hydrogenation catalyst, at a temperature of 150 to 300.degree. C and under a pressure of from 20 to 150 atmospheres.