Abstract Theoretical considerations concerning the elastic scattering of nucleons and pions in the GeV region are presented. Criteria for the validity of the simplest picture and a formula for constructing the optical potential from known phase shifts are given. The comparison with existing data reveals a sharp discrepancy in the case of p-p scattering at 8.5 GeV (this has been reported by Veksler in Kiev). Various possibilities to get rid of this disagreement are discussed: introduction of the real part of phase shifts (for which the dispersion relations would give a direct check), spin-dependence of nuclear interactions (which leads to predominance of the singlet state interaction), and quasi-resonance. Some remarks are added on relevant topics.