In the BACKONE equations the Helmholtz energy F is written as the sum F = F-H + F-A + F-D + F-Q, where F-H is the hard-body contribution, F-A the attractive dispersion force contribution, F-D the dipolar, and F-Q the quadrupolar contribution In Part I of this article (Muller et al, 1996a) the construction of BACKONE and its application to pure fluids were presented. In the extension to mixtures, for each term of F a specific mixing rule is used. This concept requires only one adjustable state-independent binary mixture parameter To demonstrate the feasibility of this approach, predictions of phase equilibria, including a liquid-liquid equilibrium and other thermodynamic properties, are given for 20 binary fluid mixtures from the groups: nonpolar + nonpolar; nonpolar + dipolar; nonpolar + quadrupolar; and polar + polar.