  We consider the effect of nuclear shadowing in polarized deep inelastic
scattering (DIS) on ^6LiD at small Bjorken x and its relevance to the
extraction of the deuteron spin structure function g_{1}^{d}(x,Q^2). Using
models, which describe nuclear shadowing in unpolarized DIS, we demonstrate
that the nuclear shadowing correction to g_{1}^{d}(x,Q^2) is significant.
