We introduce the anharmonic oscillator symmetry model to describe vibrational excitations in molecular systems exhibiting a 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 script D3h-triatomic molecules. © 1996 Academic Press, Inc.