  We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational
excitations in molecular systems exhibiting high degree of symmetry. A
systematic procedure is proposed to establish the relation between the
algebraic and configuration space formulations, leading to new interactions in
the algebraic model. This approach incorporates the full power of group
theoretical techniques and provides reliable spectroscopic predictions. We
illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules.
