  We obtain asymptotic equalities for least upper bounds of deviations in the
uniform metric of de la Vall\'{e}e Poussin sums on the sets
C^{q}_{\beta}H_\omega of Poisson integrals of functions from the class H_\omega
generated by convex upwards moduli of continuity \omega(t) which satisfy the
condition \omega(t)/t\to\infty as t\to 0. As an implication, a solution of the
Kolmogorov-Nikol'skii problem for de la Vall\'{e}e Poussin sums on the sets of
Poisson integrals of functions belonging to Lipschitz classes H^\alpha,
0<\alpha <1, is obtained
