The paper describes a new robust and efficient algorithm for liquid-liquid-liquid equilibria (LLLE) predictions and calculation. The architecture of the algorithm is a two-level one, and a judicious combination of a stability analysis, carried out in the first stage, with phase identification routines and liquid flash calculations, carried out in the second stage, is realised. The numerical routines require modest computational efforts and demonstrate excellent convergence characteristics. The thermodynamic model applied to a system does not influence the robustness of the new algorithm, which can treat any model and handle any number of components and phases. The usefulness and efficiency of the new algorithm is exemplified by using two model systems, a water + oil + non-ionic surfactant system and the system ethylene glycol + lauryl alcohol + nitromethane.