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One of the methods for studying the local atomic structure is X-ray absorption spectroscopy. By now, EXAFS spectroscopy has a large theoretical basis. However, the following problem may still arise when studying complex systems. When analyzing X-ray spectra of materials containing chemical elements with close atomic numbers, an overlap of the spectra of several chemical elements is observed. In this case, the EXAFS spectrum contains a superposition of different wave numbers, which makes it impossible to analyze such a spectrum using the classical Fourier transform method. Thus, there is a problem of developing a method for analyzing EXAFS spectra containing an overlap of signals from several chemical elements. A similar problem occurs not only in EXAFS spectroscopy. Previously, an algorithm for analyzing electron energy loss spectra (EXELFS) was developed. The developed method made it possible to determine the parameters of the local atomic structure from the spectra of the Cu-Mn system. In this paper, the possibility of analyzing EXAFS spectra containing a superposition of two extended fine structures in one energy range is considered. The test object was a solid solution of AuPt. The EXAFS spectrum of this system contains a superposition of the Au L3-edge signal on the Pt L3-edge. A series of numerical experiments were performed to isolate the normalized oscillating parts of Au and Pt from the overlapping EXAFS spectra of the AuPt system in order to determine the parameters of the local atomic structure.