Search for baryonium and the physics at FAIR

The existence of nucleon-antinucleon quasi-bound state is indicated in two decay modes of the J/psi meson studied by BES. We discuss an explanation in a fairly traditional Paris-potential model of the nucleon-antinucleon interactions. A broad, S-wave and a narrow P-wave quasi-bound states are predicted by this model. Some existing experimental evidence and possible verifications in the future are indicated.