Nucleon-antinucleon quasi-bound states, or states coupled to these, were searched for in the days of LEAR at CERN. Nothing has been found, but broad states or states close to the threshold were not excluded.
Recent indications of the existence of quasi-bound states in the N$\overline N$ system will be presented. The BES collaboration has discovered a broad enhancement close to the p$\overline p$ threshold in the S wave, isospin 0 state formed in radiative decays of J$\psi$. Another enhancement located about 50 MeV below the threshold was found in mesonic decays of J$\psi$. In terms of the Paris potential model these findings are likely to be due to the same state. Antiprotonic atomic data provide some support for this interpretation and indicate existence of another fairly narrow quasi-bound state in a P wave.
Few clarifying experiments will be indicated.