For producing very high quality base stock and for simultaneously producing high quality middle distillates, successive hydroisomerisation and catalytic dewaxmg steps are employed wherein the hydroisomerisation is carried out in the presence of a catalyst containing at least one noble metal deposited on an amorphous acidic support, the dispersion of the metal being 20%-100%. The support is preferably an amorphous silica-alumina. Catalytic dewaxing is carried out in the presence of a catalyst containing at least one hydrodehydrogenating element (group VIII) and at least one molecular sieve selected from ZBM-30, EU-2 and EU-11.