The theoretical concepts of the two methods are similar. Consequently, comparable fundamental parameter algorithms can be developed and applied to a quantitative analysis of bulk specimens and to an investigation of thin layers by TEY and by XRFA. Whereas the sampling depth of XRFA is determined by photoelectric absorption, for TEY the escape probability of electrons reduces this quantity to values of less than 100 nm. Thus, TEY is practically a surface analytical method with sampling depths between X-ray photoelectron spectrometry and XRFA. The decrease of fluorescence yields with decreasing atomic number Z is responsible for a significant reduction of the elemental sensitivity of XRFA in the range of low-Z elements. On the other hand, the elemental sensitivity of TEY increases with decreasing Z as a consequence of the dominating contribution of KLL- and LMM-Auger electrons to measured TEY jumps. The possibility to quantify submonolayers and layers of nm thickness buried under nm layers, a nearly linear dependence of TEY signals versus the elemental concentration of multielement specimens and the EXAFS and XANES information that is contained in measured TEY responses, are valuable features of TEY. A disadvantage of TEY is the time consuming sequential data accumulation of TEY spectra when compared to energy dispersive XRFA. But due to progress in instrumentation TEY is no longer reserved to synchrotron radiation sources