Abstract: A catalyst comprising at least one zeolite (molecular sieve) chosen from the group formed by the TON structure type zeolites (Theta-1, ZSM-22, ISI-1, NU-10 and KZ-2) and at least one zeolite chosen from the group formed by the zeolites (ZSM-48, EU-2, EU-11 and ZBM-30), at least one porous mineral matrix, at least one hydro-dehydrogenating element, preferably chosen from the elements of Group VIB and Group VIII of the periodic table, is used for the conversion of hydrocarbons, in particular for the reduction of the pour point of charges containing long (more than 10 carbon atoms) linear and/or slightly branched paraffins, in particular in order to convert, with a good yield, charges having high pour points to at least one cut having a low pour point and a high viscosity index for oil bases.