This renewal grant funds theoretical research to extend liquid state theory - the Born-Green-Yvon integral equation technique- to more complex fluids (polymers and polymer mixtures). There are a number of objectives for this research. One is the greater understanding of both lattice and continuum fluids and their mixtures. Another is the determination of differences in calculated thermodynamic properties based on either the lattice or continuum theories. A final objective is to development theoretical tools which will be useful for experimentalists to interpret results. Although common in studies of simple liquids, the methods used here are unique in their application to polymers and provide a comprehensive theoretical approach which is midway between the more commonly used polymer lattice and continuum theories. %%% This theoretical research will establish rigorous models of polymer liquids and liquid mixtures which will greatly assist the interpretation of experimental results for this important class of materials. The results should also place more commonly used theories in better perspective.