Solid superacid catalysts, in the form of spheres or microspheres, consisting of a mixed sulfated oxide of zirconium and of at least one other element selected from those of group 3, group 4, group 5, group 6, group 7, group 8 group 9, group 10, group 11, group 12, group 13, group 14, group 15 and those of the series of lanthanides, alone or combined with each other, are characterized in that they are obtained by means of a sol-gel process comprising the following steps: preparing a zirconium sol, mixed with a thickening agent and optionally with the element or elements selected; adding, only when microspheres are to be obtained, a non-ionic surface-active agent, to the sol; dripping, obtaining spheres, or atomising, obtaining microspheres, the sol into a basic gelation bath; ageing the spheres or microspheres of gel thus obtained; washing the spheres or microspheres with water up to pH=9; and draining them without drying them; impregnating the spheres or microspheres of gel with an aqueous solution of ammonium sulfate or, if it is not possible to obtain cogelation of the element selected with the zirconium hydroxide, with a solution of ammonium sulfate and a salt of said element selected; drying the spheres or microspheres and calcining them in air at temperatures ranging from 450° C. to 700° C. In particular, the solid superacid catalysts, when the element of group 13 is Al, can be conveniently used for isomerizing aliphatic hydrocarbons having a low molecular weight.