  We obtain the estimates for the best approximation in the uniform metric of
the classes of $2\pi $-periodic functions whose $(\psi ,\beta)$-derivatives
have a given majorant $\omega$ of the modulus of continuity. It is shown that
the estimates obtained here are asymptotically exact under some natural
conditions on the parameters $\psi ,$ $\omega $ and $\beta $ defining the
classes
