In this paper relations between the shapes of the liquid-liquid critical curves in ternary systems and the temperature characters of the heterogeneous regions are discussed.The regular-solution model with temperature-dependent parameters was employed to describe critical curves of liquid-liquid equilibria in ternary systems. Relations for the limiting values of the slopes of critical curves were derived. The corresponding type of the critical curve and consequently the temperature character of the liquid-liquid equilibrium can be deduced from these values. Model calculations were performed for ternary systems characterised by two binary subsystems with either an upper critical solution temperature or with a lower critical solution temperature, and the third binary subsystem which is homogeneous in the considered temperature range. In the calculations the following approach was used: the behaviour of two binary systems was fixed by the temperature dependencies of their parameters and ternary critical curves of LLE were then calculated for variants differing in non-ideality (deviations from the Raoult's law) of the third homogeneous binary subsystem. It was found that the level of non-ideality of the homogeneous system can influence the shape of the critical curve significantly. (C) 2003 Elsevier Science B.V. All rights reserved.