>The Logunov dispersion relation for production amplitudes is discussed. It is shown that this relation is invalid, i.e., that the production amplitude has complex singularities when regarded as a function of the Logunov variables. The reaction pi + N yields pi + pi + N is analyzed by perturbation theory, and it is found that 4 of the 5 independent variables of the reaction are ignored in the Logunov calculations. The singularities in the Logunov production amplitudes are demonstrated in Feynman diagrams. (T.F.H.)