  We have computed a grid of high resolution synthetic spectra for cool stars
(2500<Teff<6000 K) in the wavelength range 6000 -- 10200A, by employing an
updated line list of atomic and molecular lines, together with state-of-the-art
model atmospheres.
  As a by-product, by fitting TiO bandheads in spectra of well-known M giants,
we have derived the electronic oscillator strengths of the TiO gamma prime,
delta, epsilon and phi systems. The derived oscillator strenghts for the gamma
prime, epsilon and phi systems differ from the laboratory and ab initio values
found in the literature, but are consistent with the model atmospheres and line
lists employed, resulting in a good match to the observed spectra of M giants
of known parameters.
  The behavior of TiO bands as a function of the stellar parameters Teff, log g
and [Fe/H] is presented and the use of TiO spectral indices in stellar
population studies is discussed.
