The contribution of nucleon-antinucleon states (real and virtual) to electron-positron annihilation near the N̄N threshold is investigated theoretically. The nucleon electromagnetic form factor in the time-like region is calculated within the coupled-channels model. Its behaviour is shown to be predominantly denned by the nuclear N̄N interaction in the initial state. The neutron form factor does not exceed the proton one. New experimental data, revealing the existence of minima in many-pionic e +e - annihilation cross section near the N̄N threshold, are described. An analysis of the observed irregularity shows an existence of the narrow state in the N̄N system with the mass approximately 1800 MeV and the width about 15 MeV.