  We propose a q-deformed model of the anharmonic vibrations in diatomic
molecules. We analyse the applicability of the model to the phenomenological
Dunham's expansion by comparing with experimental data. Our methodology
involves a global consistency analysis of the parameters that determine the
q-deformed system, when compared with fitted vibrational parameters to 161
electronic states in diatomic molecules. We show how to include both the
positive and the negative anharmonicities in a simple and systematic fashion.
