The authors consider the effect of the quadratic Doppler term on the inhomogeneous complex optical susceptibility of a two-level system for a weak beam in the presence of a saturating, counter-propagating wave, with both waves at the same frequency. There is a red shift of the resonance frequency in the absorption as well as in the dispersion. That red shift is a function of the temperature of the medium and the degree of saturation. An asymmetry of the absorption and dispersion curves is also observed which becomes stronger when the authors approach relativistic velocities of the particles. They also study for comparison purposes the effect of the quadratic Doppler term in the particular case of only one strong beam, without the weak one. They show the different behaviour of the red shift between the two cases.