A process for the preparation of a base oil and middle distillate which is stable to oxidation and low temperature from a mineral oil fraction having a boiling range above 350.degree. C., by, in a first step, converting the mineral oil fraction on a hydrocracking catalyst under hydrocracking conditions to an extent of from 20 to 80% by weight into fractions which boil below 360.degree. C., separating the reactor effluent, if necessary, into liquid and gas phases in a high-pressure separator, treating the entire reactor effluent or only the liquid phase, directly or after removal of the fractions boiling below 360.degree. C. by distillation, in a second step with hydrogen at from 200.degree. to 450.degree. C. and at from 20 to 150 bar in the presence of a catalyst which contains a crystalline pentasil-type borosilicate zeolite, alumina and/or amorphous alumosilicate as the carrier material and one or more metals from Group VIb and/or Group VIII of the Periodic Table and phosphorus, and, after distillation of the hydrogenation product, obtaining a middle distillate in the boiling range from 180.degree. to 360.degree. C. having a pour point of below -30.degree. C. and an oxidation-stable residue having a boiling point >360.degree. C., a viscosity index of from 110 to 135 and a pour point of below -12.degree. C.