[en] Up to now it has been impossible to explain the S,T,U-enhancements of the elastic and total inelastic nucleon(N)-antinucleon(anti N)-scattering cross-sections within the 'One Boson Exchange Potential'(OBEP)-model supplemented by some phenomenological procedure taking into account the strong inelasticity of the N anti N-interaction. The reasons for this failure of the model are investigated in this work. It is done along three lines: Firstly by a closer inspection of the selfconsistency of the semiphenomenological N anti N-OBEP-model; secondly by a partial-cross-section analysis of the empirical N anti N-scattering data, which allows to extract an approximate range of annihilation processes; thirdly by the calculation of the p-wave contribution of the meson-theoretical 'two pion annihilation box'-graph to elastic N anti N-scattering. It is shown that the range of the box-graph is around ten times larger than is expected from the heuristic time-energy uncertainty argument. This is in accordance with the empirical value of the annihilation range, which is obtained. From this dominant role of the annihilation processes it is concluded that the N anti N-OBEP-model must be supplemented by some theory-inspired annihilation model instead of a purely phenomenological one to be able to explain the Baryonium resonances, if this is possible at all within the framework of meson theory. (Author)