The two-nucleon problem is discussed from the standpoint of the double dispersion relations. The analytic structure of partial wave amplitudes is completely analyzed. This is greatly facilitated by the use of the Jacob-Wick helicity amplitudes. The program of generating a set of dynamical equations by use of the unitarity condition is carried out. In the present approximation only one- and two-pion exchanges are considered; the resulting system of equations should be adequate for energies below about 170 Mev. The problem of computing the deuteron parameters is discussed. The general structure of the more complicated nucleon-antinucleon system is briefly treated.