SINGULAR PARTS OF THE RELATIVISTIC FREE-FREE NON-DIPOLE MATRIX ELEMENTS A.V.Korol$^{\ast\sharp}$ and Igor A.Solovjev$^\ast$ $\ast$ Russian Maritime Technical University, St Petersburg, Russia 198262 $\sharp$ Institut fur Theoretische Physik der Universitat Frankfurt am Main, 60054 Frankfurt/M, Germany The singular parts of the free-free single-photon matrix elements are exactly calculated for the first time for the case of relativistic projectile scattering in the field of a short-range potential. The use of the obtained results for the approximate evaluation of many-photon relativistic matrix elements is discussed.