The equilibrium of three liquid phases in a binary mixture implies the existence of tie lines and binodals that are different from the normal experimentally observable ones. First of all, there are the metastable extensions of the binodal built up by S/S tie lines. These S/S tie lines fulfill the equilibrium condition of the minimum of the Gibbs energy of the entire two-phase system. Both coexisting phases are located within the meta(stable) region, There are two additional types of tie lines : U/U (maximum of the Gibbs energy; both end points within the unstable area) and U/S tie lines (saddle point; one end point within the (meta)stable, the other within the unstable region). All types of tie lines fulfill the condition that the chemical potentials of each component have to be equal in the two phases given by the end points of the tie line. It is shown how all these tie lines build up the binodal and which rules they have to obey. A method for the calculation of all types of tie lines is presented that requires only the knowledge of the Gibbs energy of mixing; there is no need to calculate the chemical potentials. The method is applied to a Sanchez-Lacombe lattice fluid, and a polymer solution described by an extended Flory-Huggins model accounting for nonpolar and polar interactions.