The paper describes basic steps of the automatic element identification algorithm implemented in the "KSAF" and "SRDE" Energy Dispersive X-ray Fluorescence (EDXRF) analytical systems manufactured in the Soltan Institute for Nuclear Studies. The aim of the algorithm was to establish - without any operator's intervention - a list of elements present in the analyzed sample, provided that a list of peaks is already available {such a list is produced in KSAF and SRDE systems by a spectrum analysis algorithm described elsewhere). Each, analytical peak is assigned a set of line/element identification proposals (ID's) based on built-in libraries of characteristic X-ray energies; all the ID's form a list of candidate elements for the analyzed sample. According to the observed sequence of lines the elements on the list are divided into three categories: elements DISREGARDED (a higher intensity line missing), elements PROBABLE (a sequence of lines detected), elements POSSIBLE (those which can neither be disregarded nor qualified as PROBABLE). Due to relatively poor energy resolution of EDXRF systems (in comparison with e.g. wavelength dispersive XRF systems) the automatically produced results may in many cases remain inconclusive. Therefore it was found that the implemented and described herein algorithm is best used as a tool helping to concentrate operator's attention on those assignments "peak in spectrum <=> element in sample" which are doubtful or difficult for automatic establishing.