While Hamiltonians written in terms of position and momentum provide a transparent picture of the motion of a system, Hamiltonians written in terms of Lie algebras are easier to handle quantum mechanically. Therefore we are interested to know how to transform one into the other. Since the exact transformation often leads to complicated expressions, we look for approximations which preserve the essential features. As basic criterion we look for the degree of equality of the classical phase space structures. We illustrate our ideas for the case of two coupled Morse systems and its approximation in terms of the Lie algebra su(2), which is relevant to anharmonic models of molecular spectroscopy. (c) 2001 American Institute of Physics.