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For the functions from sets $C_\beta^\psi C$ and $C_\beta^\psi L_s, \ 1\leqs\leq\infty$, generated by sequences $\psi(k)>0$ satisfying the conditiond'Alembert $\mathop {\rm\lim}\limits_{k\rightarrow\infty}\frac{\psi(k+1)}{\psi(k)}=q, \ q\in[0,1)$,asymptotically unimprovable estimates for deviations of de la Vall\'{e}ePoussin sums in the uniform metric, which are represented in terms of values ofthe best approximations of $(\psi,\beta)$-differentiable functions of this sortby trigonometric polynomials in the metrics $L_s$ are obtained. Proved thatreceived estimates are unimprovable on some important functional subsets.

Lebesgue-type inequalities for de la Vallee Poussin sums on the sets of analytic and entire functions