Computer-based simulations of a reverse-flow reactor should be carried out till the attainment of the so-called cyclic steady state. Usually this state is achieved by the method of direct dynamic simulations. In the paper of Unger et al. (Comput. Chem. Eng. 21 (1997) 5167.) special approaches, making use of various minimization algorithms based most often on Newton algorithms, are proposed. In the present paper one deals with a comparison and an appraisal of these methods, applied to the reverse-flow catalytic combustion of methane that occurs in coal-mine ventilation air. (C) 2004 Elsevier Ltd. All rights reserved.