  The determination of the spin distribution functions for the neutron requires
an understanding of the changes induced by a nuclear medium. We present the
first estimates of the changes induced in the spin-dependent, valence parton
distributions of the proton and neutron bound in $^3$He and $^6$Li. For $^3$He
the result is quite reassuring, in that the off-shell correction to $g_{1n}$ is
very small. On the other hand, in $^6$Li the corrections to the spin
distributions in the bound proton are sufficiently large that they should be
taken into account if one aims for a precision of better than 10%. We provide a
simple parametrization of the off-shell changes in the valence spin
distributions of $^3$He and $^6$Li, which can be used with any conventional
estimate of nuclear binding and Fermi motion corrections.
