The CO and CO(2) carbon and oxygen Auger spectra have been measured by electron impact and compared with accurate theoretical calculations accounting for the effects of the dynamics of the nuclei on the energy and linewidth of the Auger bands. The calculations for CO were previously published [L. S. Cederbaum et al., J. Chem. Phys. 95, 6634 (1991)], while for CO(2) they are new and presented here for the first time. For both molecules, particular attention has been paid to the low-kinetic-energy region of the spectra, which corresponds to doubly charged ion states with the two holes mainly localized in the inner valence region. New bands have been observed. It is shown that a proper consideration of the vibrational broadening and shift of the bands due to the dynamics of the nuclei is needed to assign these features. For CO, very large energy shifts between corresponding features in the C 1s and O 1s spectra have been observed, confirming the theoretical predictions of 1991. The new computed spectra of CO(2) allow a very accurate analysis of the experiments over the whole energy range.