  For the functions from sets $C_\beta^\psi C$ and $C_\beta^\psi L_s, \ 1\leq
s\leq\infty$, generated by sequences $\psi(k)>0$ satisfying the condition
d'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}e
Poussin sums in the uniform metric, which are represented in terms of values of
the best approximations of $(\psi,\beta)$-differentiable functions of this sort
by trigonometric polynomials in the metrics $L_s$ are obtained. Proved that
received estimates are unimprovable on some important functional subsets.
