In the present project the degree of linear polarization of fluorescence in molecular ions populated via the Auger decay of Raman regime resonantly excited inner-shells of the NO and CO molecules will be studied theoretically and experimentally for the first time. In the NO molecule we will focus on the Auger decay of the N*O and NO* resonances into the A state of the NO+ ion investigating the intensities and the degree of polarization of the individual NO+(A - X) fluorescence bands appears in the VUV range. In the CO molecule we will concentrate on the Auger decay of the C*O and CO* resonances into the A state of the CO+ ion analyzing the intensities and degree of polarization of the individual CO+(A - X) fluorescence bands appears in the visible fluorescence range. Experimental analysis of the degree of linear polarization of emitted fluorescence will be performed by means of the Photon-Induced Fluorescence Spectroscopy method utilizing synchrotron radiation. The configuration interaction approach based on the core and valence molecular orbitals obtained within the MO LCAO method and continuum molecular orbitals obtained within the Single Center technique will be applied in order to interpret the observed fluorescence spectra. It is expected, that angular distribution of the fluorescence emission can elucidate a strong interference between closely neighbouring vibronic (lifetime vibrational interference) and electronic (electronic state interference) states overlapping within their natural lifetime widths even in the cases with the condition of small interference (e.g., in the inner-shell N*O and C*O excitations), were the interference effects were not observed previously by measuring the Resonant Auger spectra.