All ab initio Auger spectra of HF and LiF molecules are presented; no fitting procedures are involved. The energy positions of the Auger bands are calculated in two steps. First, the vertical ab initio energies were calculated by a Green function method. Second, the shift of the energy position due to the vibrational motions in the core-ionized intermediate state and in the final dicationic states were taken into account. The molecular continuum wave of the Auger electron was computed in order to evaluate the ab initio Auger rate of each main line. The widths of the bands are determined from their vibrational motions and the finite lifetime of the core-ionized state. The generated spectra are in good agreement with the experimental data.