The perturbed-chain SAFT (PC SAFT) equation of-state is applied to pure associating components as well as to vapor-liquid and liquid-Equid equilibria of binary mixtures of associating substances. For these substances, the PC-SAFT equation of state requires five pure-component parameters, two of which characterize the association. The pure-component parameters were identified for 18 associating substances by correlating vapor pressure and liquid density data. A comparison to an earlier version of SAFT confirms the good results for pure substances. When only one associating compound is present in a mixture, the PC SAFT equation of state does not require mixing rules for the association term. Using one binary interaction parameter k(ij) for the dispersion term only, the model was applied to azeotropic and nonazeotropic vapor-liquid equilibria at low and at high pressures, as well as to liquid-liquid equilibria. Simple mixing and combining rules were adopted for mixtures with more than one associating compound, introducing no additional binary interaction parameter. The simultaneous description of liquid-liquid and vapor-liquid equilibrium was also, possible with, a single. kij parameter.