Expressions for predicting pure-component and cross second virial coefficients for simple and complex systems have been developed from the bound-pair formalism of Stogryn and Hirschfelder. For pure components, the generalized correlation requires the critical temperature and pressure, Thompson's mean radius of gyration or the parachor, dipole moment, and, if appropriate, a parameter to describe chemical association which depends only in the type of group (hydroxyl, amine, ester, carboxylic acid, etc.). Mixing rules have been developed for predicting cross coefficients and solvation effects can be accounted for in a similar manner to association. Agreement with experimental data on 39 nonpolar and 102 polar and associating compounds, 119 mixed nonpolar systems, and 73 mixed systems involving polar compounds, is comparable to or better than that of several other correlations including those which require data to obtain parameters. The method should be most accurate for systems of complex molecules where no data are available In order to accurately predict phase equilibria involving the vapor phase at pressures above atmospheric, deviations from the perfect-gas law usually need to be taken into account (Prausnitz, 1969; Nagata and Yasuda, 1974). The vinal equation terminated at the second coefficient is a simple but accurate method for conditions up to a density of about one-half the critical and has been employed in completely developed methods for predicting vapor-liquid equilibria such as Prausnitz et al. (1967). Several analytical methods for predicting values for the second virial coefficient have been developed (Black, 1958; O'Connell and Prausnitz, 1967; Kreglewski, 1969; Nothnagel et al., 1973; Tsonopoulos, 1974), but except for the last, all suffer from the disadvantage of often requiring one or more parameters that must be obtained from data, or the results are too inaccurate to be acceptable. This work develops an accurate method for predicting second virial coefficients using only critical properties and molecular parameters. all of which may usually be estimated from molecular structure to the required accuracy. From extensive comparisons with pure component and cross vinal coefficient data, the present method appears to be more consistently accurate than any other purely predictive method. In addition, for strongly associating substances, the method predicts association effects at higher densities in a realistic fashion (Nothnagel et al., 1973) using a parameter which depends only on the group interaction.