Any strictly homogeneous symplectic manifold $M$ with a group of motions $\mathscr G$ may be considered as an orbit of the coadjoint action of $\mathscr G$ . Therefore all Hamiltonian systems defined on an orbit, in particular Euler's equations, are carried over to $M$ in a natural way. In this paper a multiparameter family of systems of Euler equations is constructed on $M$ , and their complete integrability (in the Liouville sense) is proved. Bibliography: 6 titles.