  A Fermi resonance-algebraic model is proposed for molecular vibrations, where
a U(2) algebra is used for describing the vibrations of each bond, and Fermi
resonances between stretching and bending modes are taken into account. The
model for a bent molecule XY_2 and a molecule XY_3 is successfully applied to
fit the recently observed vibrational spectrum of the water molecule and arsine
(AsH_3), respectively, and results are compared with those of other models.
Calculations show that algebraic approaches can be used as an effective method
for describing molecular vibrations with small standard deviations.
