Insights into the electronic structure of galvinoxyl - a prototype persistent free radical species - are of interest to elucidate its attractive photophysical and magnetic properties and to pave way for a sensible design of novel applications. To this end, we study the photoionization and photoexcitation UPS, XPS and NEXAFS spectra of the gas-phase galvinoxyl in the valence and core (C 1s and O 1s) regions using synchrotron X-ray radiation. We observe significant variations of relative band intensities with photon energy for valence ionizations below 10 eV which are rationalized in terms of the properties of the corresponding valence molecular orbitals. We calculate the core electron binding energies and core-excited states by employing the spin-unrestricted ΔDFT (B3LYP, M06-2X, and ωB97xD) and time-dependent DFT (SRC2-BLYP) methods. A good correlation between the calculations and the measured C 1s and O 1s XPS and NEXAFS spectra is obtained if one assumes that the galvinoxyl sample has undergone a partial degradation (around 50%) to the saturated (closed-shell) phenolic-quinonic derivative known as galvinol. We carry out a comparative theoretical analysis of the XPS and NEXAFS spectra of galvinoxyl and galvinol by assigning the relevant absorptions and pointing out the most important relative differences. The calculations identify a band in the O 1s NEXAFS spectrum whose diminishing intensity is a most manifest indicator of the extent of the degradation. Such a feature may thus prove useful in monitoring the scavenging dynamics of galvinoxyl using the core-excitation spectroscopy.