The structure of acetone and dimethyl sulfoxide in the liquid phase is investigated using Monte Carlo simulations and MM2 calculations. The principal site - site correlations and degree of structure in both liquids have been investigated. The results showed that dimethyl sulfoxide is more structured than acetone. At short distances the dipoles of neighboring molecules are found to be in antiparallel configurations, but further apart the molecules tend to be aligned predominantly as head to tail. In both liquids there is evidence of strong methyl - oxygen interaction, important to the structure of the liquids. The contacts suggest weak hydrogen bonds between methyl hydrogen and oxygen.