In a method presented by Lang and Wenzel [E. Lang, H. Wenzel, Extension of a cubic equation of state to solids, Fluid Phase Equil. 51 (1989) 101] an associated species is used to account for a solid phase in phase equilibrium calculation by an equation of state. In binary systems, the method was also shown to allow for solid solutions. An equation of state by Schmidt and Wenzel [G. Schmidt, H. Wenzel, A modified van der Waals type equation of state, Chem. Engng Sci. 35 (1980) 1503], modified by Peschel and Wenzel (SM)[W. Peschel, H. Wenzel, Equation of state predictions of phase equilibria at elevated pressures in mixtures containing methanol, Ber. Bunsenges. Phys. Chem. 88 (1984) 807], was used. In the present paper, new association models are given for pure carbon tetrachloride, argon and biphenyl, while modified models are given for CO2 and benzene. Some association models were made on the basis of the Peng-Robinson (PR)[D.-Y. Peng, D.B. Robinson, A new two-constant equation of state, Ind. Engng Chem. Fundam. 15 (1976) 59] equation of state. Gas-solid equilibrium calculations of binary systems involving some of these substances are compared with experimental data ta ken from the literature. The systems are. CCl4-CF4; naphthalene-CO2; naphthalene-ethylene; and biphenyl-CO2. Plots of fugacity coefficients are shown to explain the appearance of a second condensed phase in a pure component. It is also shown that the chemical equilibrium equation of association has three roots, and this is the reason why the assumption of an oligomer leads to the appearance of an additional, highly aggregated phase, especially at low temperatures.