Scanning tunneling microscopy has been performed on the 2,4-dioxopyrimidines, uracil and thymine, which self-assembled into monolayers on heated surfaces of highly oriented pyrolytic graphite and molybdenum disulfide. Our results suggest that the structures of these adsorbates, on both surfaces, are two-dimensional hydrogen-bonded networks with intermolecular configurations almost identical to those predicted by electrochemical studies of these compounds at the mercurywater interface and determined by X-ray crystallography of their respective three-dimensional solids.