  We establish the exact-order estimates of uniform approximations by the
Zygmund sums $Z^{s}_{n-1}$ of $2\pi$-periodic continuous functions $f$ from the
classes $C^{\psi}_{\beta,p}$.These classes are defined by the convolutions of
functions from the unit ball in the space
  $L_{p}$, $1\leq p<\infty$, with generating fixed kernels
  $\Psi_{\beta}(t)=\sum_{k=1}^{\infty}\psi(k)\cos\left(kt+\frac{\beta\pi}{2}\right)$,
  $\Psi_{\beta}\in L_{p'}$, $\beta\in \mathbb{R}$, $1/p+1/p'=1$. We
additionally assume that the product
  $\psi(k)k^{s+1/p}$ is generally monotonically increasing with the rate of
some power function, and, besides, for $1< p<\infty$ it holds that
  $\sum_{k=n}^{\infty}\psi^{p'}(k)k^{p'-2}<\infty$, and for $p=1$ the following
condition is true
  $\sum_{k=n}^{\infty}\psi(k)<\infty$.It is shown that under these conditions
Zygmund sums $Z^{s}_{n-1}$ and Fejer sums \linebreak$\sigma_{n-1}=Z^{1}_{n-1}$
realize the order of the best uniform approximations by trigonometric
polynomials of these classes.
