The BACKONE equations area family of physically based equations of state, in which the Helmholtz energy (F) is written as a sum of contributions from characteristic intermolecular interactions. For dipolar fluids F is given by the DIBACKONE equation as F = F-H + F-A + F-D, where F-H is the hard-body contribution, F-A the attractive dispersion force contribution, and F-D the dipolar contribution. For quadrupolar fluids F is given by the QUABACKONE equation as F = F-H + F-A + F-Q, where F-Q is the quadrupolar contribution. F-D and F-Q have been determined on the basis of extensive molecular simulations [B. Saager, J. Fischer, Fluid Phase Equilibria, 72 (1992) 67-88]. Both the DIBACKONE and the QUABACKONE equation need only four substance specific parameters : a characteristic temperature T-0, a characteristic density rho(0), an anisotropy parameter ct and either a reduced squared dipole moment mu(*2) or a reduced squared quadrupole moment Q(*2). In the present work these parameters were determined for the alternative refrigerants R123, R124, R125, R134a, R143a, R152a, R218, and R236ea by fitting them to saturated liquid densities and vapour pressures at four temperatures. It turned out that all these substances can be quite well described by the QUABACKONE equation with the exception of R152a which is better described by DIBACKONE. Moreover, a description in the form of F = F-H + F-A + F-Q + F-D with five parameters called D + QBACKONE is explored. Comparisons of the BACKONE results for the saturated liquid densities, the saturated vapour densities and the vapour pressures with experimental data or with data from reference Helmholtz function (RHF) equations show satisfying agreement. For R123, R125, R134a, and R152a enthalpies and entropies for coexisting Liquid and vapour states are also compared with RHF equation results and show maximum relative deviations in the enthalpy of less than 1.5% and in the entropy of less than 1.3%. Moreover, coefficients of performance for an idealized refrigeration and a heat pump cycle are compared with RHF equation results and show for R134a deviations less than 0.25% and for R152a deviations less than 1.00%. Finally, a thermodynamic table is given for R236ea on the basis of BACKONE. (C) 1998 Elsevier Science B.V. All rights reserved.