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The nuclear effects in the spin-dependent structure functions $g_1^D$ and$b_2^D$ are calculated in the relativistic approach based on the Bethe-Salpeterequation with a realistic meson-exchange potential.  The results of calculations are compared with the non-relativisticcalculations. The problem of extraction of the neutron spin structure function,$g_1^n$, from the deuteron data is discussed.Comment: (Talk given at the SPIN'94 International Symposium, September 15-22,  1994, Bloomington, Indiana), 6 pages, 5 figures, Preprint Alberta Thy 29-9

The deuteron spin structure functions in the Bethe-Salpeter approach and the extraction of the neutron structure function gn1(x)