An exoskeletal system for assistance of the movement of intra-extra rotation of a shoulder of a user comprising an upper limb exoskeleton having a rotational joint of abdo-adduction, and a support frame connected to said upper limb exoskeleton, said support frame comprising: - a containment shell; - a slide; - a kinematical chain comprising: - a first link connected to said slide through a first rotational joint having a rotation axis z, said slide arranged to allow a translation of said first rotational joint along said rotation axis z with respect to said containment shell; - a second link connected to said first link through a second rotational joint having rotation axis z' parallel to said rotation axis z, said second link being connected to said rotational joint of abdo-adduction of said upper limb exoskeleton by a third rotational joint having rotation axis z" parallel to said rotation axis z; in such a way that said rotational joint of abdo-adduction of said upper limb exoskeleton is arranged in a plurality of relative spatial positions with respect to said containment shell, said exoskeletal system characterized in that said support frame comprises a weight balancing system comprising said slide connected to at least one counterweight by a pulley, said at least one counterweight having mass equal to the sum of the masses of said kinematical chain and of said upper limb exoskeleton, in such a way that said slide maintains its own equilibrium position along said rotation axis z, and in that said first rotational joint is arranged to carry out a rotation of 180° about said rotation axis z, allowing to arrange the exoskeleton near both the upper limbs of the user. frame connected to said upper limb exoskeleton, said support frame comprising: - a containment shell; - a slide; - a kinematical chain comprising: - a first link connected to said slide through a first rotational joint having a rotation axis z, said slide arranged to allow a translation of said first rotational joint along said rotation axis z with respect to said containment shell; - a second link connected to said first link through a second rotational joint having rotation axis z' parallel to said rotation axis z, said second link being connected to said rotational joint of abdo-adduction of said upper limb exoskeleton by a third rotational joint having rotation axis z" parallel to said rotation axis z; - a containment shell; - a slide; - a kinematical chain comprising: - a first link connected to said slide through a first rotational joint having a rotation axis z, said slide arranged to allow a translation of said first rotational joint along said rotation axis z with respect to said containment shell; - a second link connected to said first link through a second rotational joint having rotation axis z' parallel to said rotation axis z, said second link being connected to said rotational joint of abdo-adduction of said upper limb exoskeleton by a third rotational joint having rotation axis z" parallel to said rotation axis z; - a first link connected to said slide through a first rotational joint having a rotation axis z, said slide arranged to allow a translation of said first rotational joint along said rotation axis z with respect to said containment shell; - a second link connected to said first link through a second rotational joint having rotation axis z' parallel to said rotation axis z, said second link being connected to said rotational joint of abdo-adduction of said upper limb exoskeleton by a third rotational joint having rotation axis z" parallel to said rotation axis z; in such a way that said rotational joint of abdo-adduction of said upper limb exoskeleton is arranged in a plurality of relative spatial positions with respect to said containment shell, said exoskeletal system characterized in that said support frame comprises a weight balancing system comprising said slide connected to at least one counterweight by a pulley, said at least one counterweight having mass equal to the sum of the masses of said kinematical chain and of said upper limb exoskeleton, in such a way that said slide maintains its own equilibrium position along said rotation axis z, and in that said first rotational joint is arranged to carry out a rotation of 180° about said rotation axis z, allowing to arrange the exoskeleton near both the upper limbs of the user.