For Hydroisomerizering charges emanating from the Fischer-Tropsch process:a) hydrogen is reacted with the charge in contact with a catalyst 1 in a first reaction zone, the catalyst 1 comprising at least one alumina-based matrix and at least one hydro-dehydrogenation component andb) the effluent from the first reaction zone is put into contact with a catalyst 2 in a second reaction zone, the catalyst 2 comprising:20 to 97% by weight of at least one matrix,3 to 80% by weight of at least one Y zeolite in hydrogen form, the zeolite being characterized by an SiO.sub.2 /Al.sub.2 O.sub.3 molar ratio of over 4.5; a sodium content of less than 1% by weight determined at 1100.degree. C. under calcining conditions; an a.sub.o crystal parameter of the elemental mesh of less than 24.70.times.10.sup.-10 m; and a specific surface area determined by the BET method of over 400 m.sup.2.g.sup.-1, andat least one hydro-dehydrogenation component.