The invention concerns a method for .alpha.-olefin trimerization comprising a number of carbon atoms not less than 3, by transforming an .alpha.-olefin or a hydrocarbon mixture containing .alpha.-olefins, at temperatures ranging between 0 and 150.degree. C. and pressures ranging between 1 and 200 bars, in the presence of a catalyst. Said method uses a catalyst capable of being produced from: a) a compound of formula RMX3, wherein: R represents a cyclopentadienyl group whereof the hydrogen atoms can be partly or entirely substituted by identical or different alkyl groups and/or aryl groups, two substituents being capable of further forming a saturated or unsaturated hydrocarbon chain; M represents a titanium, zirconium or hafnium atom; and the groups X represent independently of one another extractable counter-ions; and b) at least an activating adjuvant. The invention further concerns the resulting trimers, alkanes capable of being produced with said trimers by hydrogenation, oxo-alcohols capable of being produced from said trimers, plasticizers and surfactants capable of being produced from said oxo-alcohols, as well as lubricants and fuel additives containing said trimers and/or said alkanes.