Process for the contemporaneous production of fuels and lubricating bases from synthetic paraffinic mixtures, which includes a hydrocracking step in the presence of a solid bi-functional catalyst comprising: (A) a support of an acidic nature consisting of a catalytically active porous solid, including silicon, aluminum, phosphorus and oxygen bonded to one another in such a way as to form a mixed amorphous solid characterized by an Si/Al atomic ratio of between 15 and 250, a P/Al ratio of at least 0.1, but lower than 5, a total pore volume ranging from 0.5 to 2.0 ml/g, with an average pore diameter ranging from 3 nm. to 40 nm, and a specific surface area ranging from 200 to 1000 M2/g; (B) at least one metal with a hydro-dehydrogenating activity selected from groups 6 to 10 of the periodic table of elements, dispersed on said support (A) in an amount of between 0.05 and 5% by weight with respect to the total weight of the catalyst.