Electron Raman scattering of light has been observed recently in many high-temperature superconductors. At temperatures below the critical value there is a clear reduction in the scattering cross section at low transferred frequencies. In contrast to the theoretical predictions, there is no threshold which could be linked to the gap in the electron spectrum. This behavior of the scattering, and particularly its dependence on the transferred frequency, can be explained if we assume that the gap vanishes along certain lines on the Fermi surface.