  A Hamiltonian dynamics defined on the two-dimensional hyperbolic plane by
coupling the Morse and Rosen-Morse potentials is analyzed. It is demonstrated
that orbits of all bounded motions are closed iff the product of the parameter
$\tilde a$ of the Morse potential and the square root of the absolute value of
the curvature is a rational number. This property of trajectories equivalent to
the maximal superintegrability is confirmed by explicit construction of
polynomial superconstant of motion.
