  Antiproton scattering off $^3\He$ and $^4\He$ targets is considered at beam
energies below 300 MeV within the Glauber-Sitenko approach, utilizing the $\bar
N N$ amplitudes of the J\"ulich model as input. A good agreement with available
data on differential $\bar p ^4\He$ cross sections and on $\bar p ^3\He$ and
$\pbar ^4\He$ reaction cross sections is obtained. Predictions for polarized
total $\bar p ^3$He cross sections are presented, calculated within the
single-scattering approximation and including Coulomb-nuclear interference
effects. The kinetics of the polarization buildup is discussed.
