Analysis of core-loss spectra in electron energy-loss spectroscopy associated with transmission electron microscopy (TEM-EELS) is introduced as a tool giving information equivalent to X-ray absorption fine structure (XAFS) on nano-scale areas. After briefly describing the principle of TEM-EELS, including extended energy-loss fine structure (EX-ELFS) and energy-loss near edge structure (ELNES), merits and demerits of TEM-EELS are compared to those of XAFS analysis. A new analysis method applying the ‘wavelet transformation’ is introduced. This method is effective particularly to isolate the signals from the original EXELFS spectrum containing noises and artifacts. Furthermore, information on higher-order coordination shells and many-body correlations can be extracted from the EXELFS interference function, using the wavelet transformation. As an application example of this method, we show characterization of local structural relaxation of amorphous silicon by intense X-ray illumination. Finally some future prospects of TEM-EELS are briefly mentioned.