The spectrum of electrons elastically backscattered from the surface and within its vicinity reflects the probability of electron elastic backscattering on the surface atoms, quasi-elastic scattering and the inelastic scattering visible in the low energy side of the elastic peak. The method for investigating the processes of electron elastic backscattering on the surface atom is called the elastic peak electron spectroscopy (EPES).In the present work, AuNi alloys of different compositions are investigated using X-ray photoelectron spectroscopy (XPS) and the EPES method with the aid of the line shape analysis called the fuzzy k-nearest neighbour (fkNN) rule. The line shape analysis was found to be applicable for EPES spectroscopy. It allows distinguishing the surfaces exhibiting various surface roughness, texture and grain size, and quantifying the selected information depths. The quantitative results obtained from the XPS analysis and the EPES spectra line shape analysis indicated Au surface segregation with Au surface enriched profile. Quantitative discrepancies are discussed within the non-uniform concentration profiles of constituents due to sputter cleaning and annealing, different diffusion coefficients for Au and Ni, differences in the information depths sampled by XPS and EPES methods and differences in electron elastic backscattering cross-sections for Ni and Au.