The Guggenheim nonrandom lattice-hole theory for open chain molecules was extensively studied recently and a new rigorous equation of state (EOS) was proposed by the present authors. A method was also proposed for the estimation of EOS parameters based on a group contribution (GC) applicable to large molecules. In the present study, the formalism was extended to closed chain molecules and small molecules based on the Staverman combinatory. Using the new method properties of alkanes, ethers, ketons, alcohols and their mixtures were predicted. Since the present method is an EOS method, it applies to pure systems as well as mixtures and to high pressure systems. Flash calculation results indicate that the present method is as accurate as the UNIFAC method.