Cerium doped Gd3Ga3Al2O12 (GGAG) single crystals as well as GGAG:Ce single crystals co-doped by divalent (Mg2+, Ca2+) and tetravalent (Zr4+, Ti4+) ions have been studied by means of time-resolved luminescence as well as the excitation luminescence spectroscopy in vacuum ultraviolet (VUV) and soft X-ray (XUV) spectral range. Tunable laser excitation was applied for time-resolved experiments in order to obtain luminescence decay curves under excitations in Ce3+, Gd3+ and excitonic absorption bands. The influence of the co-dopant ions on the Ce3+ luminescence decay kinetics is elucidated. The fastest luminescence decay was observed for the Mg2+ co-doped crystals under any excitation below bandgap energy indicating the perturbation of the 5d states of Ce3+ by Mg2+ ions. Synchrotron radiation was utilized for the luminescence excitation in the energy range from 4.5 to 800 eV. Special attention was paid to the analysis of Ce3+ excitation spectra in VUV and XUV spectral range where multiplication of electronic excitation (MEE) processes occur. Our results demonstrated that GGAG:Ce single crystals co-doped by Mg2+ ions as well as the GGAG:Ce crystal annealed in vacuum reveal the most efficient excitation of Ce3+ emission in VUV-XUV excitation range. The role of intrinsic defects in MEE processes in the co-doped as well as in the annealed GGAG:Ce single crystals is discussed.