<p>The so-called AQ-iteration method is proposed to resolve the nonconvergence problems in the calculation of concentration distribution in cascades by alternatively performing the Q-iteration and the Q^*-iteration. The Q^*-iteration is a Newton–Raphson method based on the gradient of the basic quantity <b>Q</b> in the Q-iteration. Numerical experiments are performed for two example cascades, for which the Q-iteration does not give convergent results. The AQ-iteration demonstrates a better performance than the Q-iteration. The results show that usually a larger under-relaxation factor gives a faster convergence. The fastest convergence is obtained when the under-relaxation factor is one, but this may occasionally yield nonconvergence. Convergence can always be obtained by choosing appropriate values of the under-relaxation factors and combination of the numbers of the Q- and Q^*-iterations in an AQ-iteration.</p>