Summary: ``In this paper, we investigate the problem of approximation of classes $C^{\overline{\psi}}_\infty$ introduced by A. I. Stepanets by the generalized Zygmund sums. Especially, we obtain asymptotic equalities that give a solution of the Kolmogorov-Nikol'skii problem for the generalized Zygmund sums on the classes $C^{\overline{\psi}}_\infty$ in several important cases.''