  We estimate the perturbative nuclear shadowing in the nuclear structure
function $F_2^A(x,Q^2)$, mainly at the kinematic region of HERA using the
Glauber-Mueller approach. The contributions of the quark and gluon sectors to
the nuclear shadowing are estimated. We predict that the nuclear shadowing
corrections are important and that saturation of the ratio $R_1 =
F_2^{A}(x,Q^2)/A F^p_2(x,Q^2)$ occurs once the shadowing in the gluon sector is
considered.
