The reactions of electron-position annihilation into nucleon-antinucleon pairs have been studied in a nonperturbative quark model. The work suggests that the two-step process, in which the primary [Formula: see text] pair forms first a meson and then the meson decays into baryon pair, is dominant over the one-step process in which the primary [Formula: see text] pair is directly dressed by two additional [Formula: see text] pairs to form a baryon pair. The experimental data indicates that there exists a vector meson with quantum numbers IG(JPC) = 0-(1--) and a mass around 2 GeV.