A ternary critical end line (T-CEL) is a line of Ternary critical end points (T-CEPs). T-CELs provide key information on the phase behavior of ternary systems, i.e., they are boundaries for the ternary three-phase equilibrium. A ternary system may have several T-CELs. It is desirable to have available a robust algorithm for computing complete ternary CELs, thus minimizing the need for user intervention. It is also important to reliably detect the key points where T-CELs originate or terminate. In this work, we propose to apply a numerical continuation method (NCM) for the fast and robust computation of T-CELs. We present calculated T-CELs for highly asymmetric systems showing the topologies that these lines define. We consider a model of the equation of state (EOS) type and use it over wide ranges of conditions. Such ranges are much wider than those previously considered in the literature. Our main conclusion is that models for the fluid phase equilibria of ternary systems may predict, for a given system, several T-CELs of varying types and topologies. Some of such topologies have been observed for the first time in this work. (C) 2014 Elsevier B.V. All rights reserved.