  We present experimental results of the first high-precision test of
quark-hadron duality in the spin-structure function g_1 of the neutron and
$^3$He using a polarized 3He target in the four-momentum-transfer-squared range
from 0.7 to 4.0 (GeV/c)^2. Global duality is observed for the spin-structure
function g_1 down to at least Q^2 = 1.8 (GeV/c)^2 in both targets. We have also
formed the photon-nucleon asymmetry A_1 in the resonance region for 3He and
found no strong Q^2-dependence above 2.2 (GeV/c)^2.
