Polarization properties of strange baryons produced in pp reactions, p + p -> p + Lambda^0 + K^+ and p + p -> p + Sigma^0 + K^$, near thresholds of the final states (p Lambda^0 K^+) and (p Sigma^0 K^+) are analysed relative to polarizations of colliding protons. The cross sections for pp reactions are calculated within the effective Lagrangian approach accounting for strong pp rescattering in the initial state of colliding protons with a dominant contribution of the one-pion exchange and strong final-state interaction of daughter hadrons (Eur. Phys. J. A 9, 425 (2000)).