We consider magnetic geodesic flows of the normal metrics on a class
of homogeneous spaces, in particular (co)adjoint orbits of compact Lie
groups. We give the proof of the non-commutative integrability of flows
and show, in addition, for the case of (co)adjoint orbits, the usual Liouville
integrability by means of analytic integrals. We also consider the
potential systems on adjoint orbits, which are generalizations of the magnetic
spherical pendulum. The complete integrability of such system is
proved for an arbitrary adjoint orbit of a compact semisimple Lie group.