Summary: The scattering amplitudes of string theory are divergent when the Riemann surface has a particular degeneracy associated with loops becoming infinitely long. These divergences originate from multiparticle intermediate states. The string amplitudes do not have the imaginary part required by unitarity. We give a prescription for defining string amplitudes that extends to all tachyon-free string theories. Explicit applications of our procedure are given at one-loop level for the Green-Schwarz and Neveu-Schwarz-Ramond theories. Our procedure is valid for higher loops also. However, only some simple features for this situation are explicitly discussed.