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The method of Doppler - free comb - spectroscopy for dipole transitions wasproposed. The calculations for susceptibility spectrum for moving two-levelatoms driving by strong counter propagating combs have been done. The usedtheoretical method based on the Fourier expansion of the components of densitymatrix on two rows on kv (v-velocity of group of atoms, k-projection of wavevector) and {\Omega} (frequency between comb components). For testing ofvalidity of this method the direct numerical integration was done. The narrowpeaks with homogeneous width arise on the background of Doppler counter. Thecontrast of these peaks is large for largest amplitudes of comb-components.Power broadening is increasing with increase of field amplitudes. The spectralrange of absorption spectrum is determined by the spectral range of combgenerator and all homogeneous lines arise simultaneously. The spectralresolution is determined by the width of homogeneously-broadening lines. Thephysical nature of narrow peaks is in the existence of multi-photon transitionsbetween manifolds of quasi-energy levels arising for different groups of atomsmoving with velocities that satisfy to the resonant conditions 2kv=(n+l){\Omega}, where n, l - are integers and {\Omega} - frequency differencebetween comb teeth.

Nonlinear Doppler - Free comb-spectroscopy in counter-propagating fields