The differential and total cross sections for annihilation of longitudinally polarized and transversely polarized electrons and positrons into pairs of longitudinally polarized protons and antiprotons are calculated in the center-of-mass system. The expressions obtained for the cross sections have electromagnetic, weak, and interference terms. It is shown that the existence of a weak current-current interaction (ēe) (-pp) must lead for protons and antiprotons, emitted at an angle ®=90° to a nonzero degree of longitudinal polarization P(E) =1.3 and 36% for E=2.5 and 10 GeV and G=GF=10-5 M-2,to the presence of "forward-backward" asymmetry in the angular distribution of the protons A(E)=1 and 12% for E=2.5 and 10 GeV (the asymmetry exists even when all the particles are unpolarized), and to other effects which are absent in the case of a pure electromagnetic interaction. It is shown that in experiments with polarized particles the contributions of different form factors can be distinguished and studied separately. © 1975 Plenum Publishing Corporation.