A tentative experimental test of the analyticity structure of theS-matrix in low-energy nucleon-nucleon scattering is performed by showing that among an appreciable number of functions describing the energy dependence of phase shifts in proton-proton scattering dynamics, satisfying various threshold and asymptotic requirements, those having qualitatively the proper analytic structure give somewhat better fits to experimental data than those with «improper» analytic structure. Statements are also made about the relative merits of various approximation schemes.