The topic of the present work is the development of a simple model for the description of phase equilibria occurring in nonideal systems, such as those containing size-asymmetric components or mixtures made of polar or associating compounds with hydrocarbons, that are capable of strong demixing. The generalized NRTL model presented in this first part derives from the lattice two-fluid theory and differs from the original model by considering the size asymmetry of mixture components; results obtained for the modeling of phase equilibria in hydrocarbon, polar, and highly immiscible systems are compared with other literature models, such as the van Laar, NRTL, and UNIQUAC models. In the second part of this work, this model is associated with the Peng-Robinson EoS using the EoS/G(E) approach based on a generalized reference state, and a new group contribution is proposed for the prediction of the binary interaction parameters.