A new type of Pendellösung Fringes due to X-ray Resonant Scattering (PFXRS) is observed for several reflections from GaAs and Ge. PFXRS is caused by a sharpe change in f' near the X-ray absorption edge. In this paper are described a condition for the observation of PFXRS, results of the measurement and a method for the determination of the f' from a modulation of PFXRS.