The solid-solid-liquid equilibrium of ternary or multicomponent systems is few explored in literature, due to their complex experimental description, and especially due to their complex modeling. Such a difficult increases in case of organic compounds, such as lipidic molecules, due to the presence of additional peritectic, and metatectic transitions, formation of solid solutions, and polymorphism. In order to fill such a lacuna, two complete SSLE fatty acids binary diagrams (linoleic acid + myristic acid and linoleic acid + stearic acid) were experimentally evaluated and modeled. Also, a third system (myristic acid + stearic acid) presented in literature was modeled, and the SSLE T-x-z phase diagram of the respective ternary system was presented. The melting properties were determined by differential scanning calorimetry, and the activity coefficients of both phases adjusted by excess Gibbs energy models by using the Crystal-T algorithm, proposed in literature. Beyond complete new SSLE experimental data, this work used a new approach for the modeling of the peritectic transition, and presents for the first time the Tammann surface, a tridimensional version of the Tammann triangle for the analysis of the enthalpy of the eutectic transition in the ternary system. (C) 2016 Elsevier B.V. All rights reserved.