  The spin structure functions of the system of quasifree fermions on mass
shell are studied in a consistently covariant approach. Comparison with the
basic formulas following from the quark-parton model reveals the importance of
the fermion motion inside the target for the correct evaluation of the spin
structure functions. In particular it is shown, that regarding the moment
$\Gamma_{1}$, both the approaches are equivalent for the static fermions, but
differ by the factor 1/3 in the limit of massles fermions ($% m \ll p_0$, in
target rest frame). Some other sum rules are discussed as well.
