Elastic scattering of antiprotons on deuteron and 3 He targets is studied within the Glauber-Sitenko theory. In case of pd scattering, the single-and double pN scattering mechanisms and the full spin dependence of the elementary pN scattering amplitudes are taken into account on the basis of an appropriately modified formalism developed for pd scattering. Differential cross sections and analyzing powers are calculated for antiproton beam energies between 50 and 300 MeV, using the N N model of the Jülich group as input. Results for total polarized cross sections are obtained via the optical theorem. The efficiency of the polarization buildup for antiprotons in a storage ring is discussed.