We investigated spin states of stable neutral pure-organic radical molecules of 1,3,5-triphenyl-6-oxoverdazyl (TOV) and 1,3,5- triphenyl-6-thioxoverdazly (TTV) adsorbed on an Au(111) surface by observing a Kondo resonance which originates from the spin- electron interaction. In scanning tunneling spectroscopy (STS) spectra, a clear Kondo resonance was detected for the TOV molecule. However for a TOV molecule with a bright spot in the occupied state image and for a TTV molecule, no Kondo resonance was detected.