Syntheses, characterization and study of cobaloximes of the type [Co(dmgH)2(R)(L)] are reported, where dmgH is dimethylglyoximato, L is 2,6-dimethylpyrazine (dmp) or 3,5-lutidine (lut), and R is an alkyl group or an inorganic monoanionic ligand. H-1-NMR spectroscopic studies on these compounds show that the upfield shifts of the alpha protons of the neutral L ligand are linearly related not only with the downfield shifts of the methylic protons of the equatorial (dmgH) ligands, but also to the wavelength (lambda(MLCT)) of the Co-->dmgH charge transfer band in the ultraviolet spectra. This type of correlations which were previously found only for cobaloximes containing inorganic ligands in the axial sites (i.e. Cl-, Br- CN-) can be explained in terms of the ''ring current'' resulting from the delocalized pi electrons of the metallacycles, and are now extended to both inorganic and organometallic bis(dimethylglyoximato)cobalt(III) complexes. A tentative interpretation of the variations observed in the C-13-NMR chemical shifts of the equatorial ligand's carbon atoms in trans-[Co(dmgH)2(R)(py)] is also presented based on the influences of the ''ring current'' of the pyridine ligand.