Abstract
The anomalous dimensions of high-twist operators in deeply inelastic scattering ($\gamma_{2n}$) are calculated in the limit when the moment variable $N \rightarrow 1$ (or $x_B\rightarrow 0$) and at large $Q^2$ (the double logarithmic approximation) in perturbative QCD. We find that the value of $\gamma_{2n}(N-1)$ in this approximation behaves as ${N_c
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