Assume that \(f(z)\) is analytic in the unit disk and has a non-tangential limit \(f(e^{i\theta})\) at a.e. point of the unit circle. The integral modulus of continuity of order \(p\), \(1\leq p < +\infty\), of the boundary function \(f(e^{i\theta})\) is \(\omega (\delta , f) = \sup_{0<|t|\leq \delta} \bigl({1 \over {2\pi}} \int_{-\pi}^{\pi} |f(e^{i(\theta + t)}) - f(e^{i\theta})|^{p}d\theta \bigr)^{1/p}\). The essential supremum is used in the usual fashion for \(\omega_{\infty}(\delta , f)\). The mean Lipschitz space \(\Lambda_{\alpha}^{p}\) consists of those functions \(f(z)\) for which \(\omega_{p}(\delta , f) = O(\delta^{\alpha})\) as \(\delta \to 0\). For a continuous and increasing function \(\omega:[0,\pi]\to [0,\infty)\) with \(\omega(0)=0\), the generalized mean Lipschitz space \(\Lambda(p,\omega)\) consists of those functions \(f(z)\) for which \(\omega_{p}(\delta , f) = O(\omega(\delta))\) as \(\delta \to 0\). For a continuous and increasing function \(\omega:[o,\pi]\to [0,\infty]\) with \(\omega(0)=0\) the generalized mean Lipschitz space \(\Lambda(p,\omega)\) consists of those functions \(f(z)\) for which \(\omega_p(\delta,f)=O(\omega(\delta))\) as \(\delta\to 0\). In Theorem 1 conditions on \(\omega(\delta)\) are given under which the class \(\Lambda(p,\omega)\), \(1