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The diffusion coefficient of a vacancy diffusing in a B2 compound via six-jump cycles is calculated by means of rate equations along a method introduced by Ishioka and Koiwa, which is more general than the mean-first-passage-time concept formerly used by Arita ct al. It is shown that the two methods yield very similar results for typical measuring temperatures. Furthermore, the ratio P-110/P-100 of the probabilities for effective jumps via (110) cycles or via (100) cycles is determined by using elementary properties of stochastic processes. The advantage of the present calculation is that no artifical restrictions on the parameters of the six-jump cycles are required. It is shown that for such general six-jump cycles no limits for P-110/P-100 can be established, so that measurements of this ratio cannot be used to figure out whether diffusion via six-jump cycles may be relevant in a specific material. The limits for the ratio D-A/D-B Of the tracer diffusion coefficients of the two constituents A and B of the compound are also reconsidered. Analogous results are obtained for the correlated three-jump cycles. (C) 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.