  We apply the Anharmonic Oscillator Symmetry Model to the description of
vibrational excitations in ${\cal D}_{3h}$ and ${\cal T}_d$ molecules. A
systematic procedure can be used to establish the relation between the
algebraic and configuration space formulations, by means of which new
interactions are found in the algebraic model, leading to reliable
spectroscopic predictions. We illustrate the method for the case of ${\cal
D}_{3h}$-triatomic molecules and the ${\cal T}_d$ Be-cluster.
