In mathematics, a superintegrable Hamiltonian system is a Hamiltonian system on a 2n-dimensional symplectic manifold for which the following conditions hold: (i) There exist k>n independent integrals F_i of motion. Their level surfaces (invariant submanifolds) form a fibered manifold over a connected open subset. (ii) There exist smooth real functions s_{ij} on N such that the Poisson bracket of integrals of motion reads . (iii) The matrix function s_{ij} is of constant corank m=2n-k on N. If k=n, this is the case of a completely integrable Hamiltonian system. The Mishchenko-Fomenko theorem for superintegrable Hamiltonian systems generalizes the Liouville-Arnold theorem on action-angle coordinates of completely integrable Hamiltonian system as follows. Let invariant submanifolds of a superintegrable Hamiltonian system be connected compact and mutually diffeomorphic. Then the fibered manifold F is a fiber bundle in tori T^m. There exists an open neighbourhood U of F which is a trivial fiber bundle provided with the bundle (generalized action-angle) coordinates , , such that (\phi^A) are coordinates on T^m. These coordinates are the Darboux coordinates on a symplectic manifold U. A Hamiltonian of a superintegrable system depends only on the action variables I_A which are the Casimir functions of the coinduced Poisson structure on F(U). The Liouville-Arnold theorem for completely integrable systems and the Mishchenko-Fomenko theorem for the superintegrable ones are generalized to the case of non-compact invariant submanifolds. They are diffeomorphic to a toroidal cylinder.