  We calculate shadowing in the process of deep inelastic interactions of
leptons with nuclei in the perturbative regime of QCD. We find appreciable
shadowing for heavy nuclei (e.g. Pb) in the region of small Bjorken scaling
variable $10^{-5}\leq x \leq 10^{-3}$. This shadowing depends weakly on $Q^2$,
but it may be strongly influenced, especially at $x \geq 10^{-3}$, by the
existence of real parts of the forward scattering amplitudes.
