Denis V. Juriev Jordan designs on Lie algebras and nonhamiltonian interaction of hamiltonian systems (15K, TeX) ABSTRACT. Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of Jordan designs on Lie algebras. Results of paper confirm the supposition that an algebraic formalism of Jordan designs on Lie algebras may be an effective tool for the description of asymptotically almost periodic dynamical systems.