A cubic equation of state (EOS) proposed by Sake, Wu and Prausnitz (SWP) [T. Sako, A.H. Wu, J.M. Prausnitz, J. Appl. Polym. Sci. 38 (1989) 1839-1858.] is used to correlate phase equilibria in systems containing small and large molecules. Two pure-component parameters are fitted to vapour pressures (volatile molecules) and to liquid density data (non-volatile molecules and polymers), respectively. New pure-component parameters for nitrogen and a series of 1-alkenes are reported. The parameter estimation procedure for polymers and polymer-like substances such as heavy n-alkanes is refined. For this purpose, the repulsion parameter b is refitted to describe the correct slope of the PV-isotherms. This was found to be necessary to improve the phase-equilibrium calculations of binary polymer systems. Binary systems of ethylene with heavy alkanes or alkenes and one ternary system (ethylene/eicosane/tetracontane) are investigated. It is shown that one temperature-independent binary interaction parameter is sufficient to describe the phase equilibrium in these binary systems. The accuracy of the correlation in systems containing a heavy alkane is comparable or better than the results obtained from the Peng-Robinson (PR) EOS.