An olefin oligomerization process employs a particular silica-alumina catalyst which comprises a non zeolitic support based on silica-alumina containing a quantity of more than 5% by weight and 95% by weight or less of silica (SiO.sub.2) and has the following characteristics: a mean pore diameter, measured by mercury porosimetry, in the range 20 to 140 .ANG.; a total pore volume, measured by mercury porosimetry, in the range 0.1 ml/g to 0.6 ml/g; a total pore volume, measured by nitrogen porosimetry, in the range 0.1 ml/g to 0.6 ml/g; a BET specific surface area in the range 100 to 550 m.sup.2/g; a pore volume, measured by mercury porosimetry, included in pores with a diameter of more than 140 .ANG., of less than 0.1 ml/g; a pore volume, measured by mercury porosimetry, included in pores with a diameter of more than 160 .ANG., of less than 0.1 ml/g; a pore volume, measured by mercury porosimetry, included in pores with a diameter of more than 200 .ANG., of less than 0.1 ml/g; a pore volume, measured by mercury porosimetry, included in pores with a diameter of more than 500 .ANG., of less than 0.1 ml/g; and an X ray diffraction diagram containing at least the principal characteristic peaks of at least one of the transition aluminas included in the group composed of alpha, rho, khi, eta, gamma, kappa, theta and delta aluminas.