For the production of high quality base oils with production of high quality middle distillates, feedstocks are obtained from the distillation of crude or from units for transformation and refining of the latter, there are provided a converting pretreatment stage of the feedstock and a catalytic dewaxing stage. The converting pretreatment stage occurs in the presence of a catalyst containing at least one noble metal deposited on an acid substrate in particular silica-alumina, to effect hydrocracking and hydroisomerization reactions. The catalytic dewaxing occurs in the presence of a catalyst with a zeolite base that is preferably selected from zeolites of the TON-structural type (theta-1, ISI-1, ZSM-22, KZ-2, NU-10), and the zeolites ZSM-48, ZBM-30, EU-2, EU-11, ferrierite, EU-1 and EU-13, and the catalyst also contains at least one hydro-dehydrogenating element.