[en] A theory of electron re-emission Moessbauer (ERM) spectroscopy has been derived, assuming exponential attenuation of the re-emitted internal conversion and Auger electrons. Simple analytic expressions are obtained for all quantities of interest in the interpretation of ERM spectra from multi-layer surface films. These include the ERM peak areas, peak widths, and electron counting rates as a function of velocity. The results are applicable for surface films containing any number of distinct layers, and are derived in terms of simple analytic functions of the layer thicknesses, peak separations, and electron and gamma ray attenuation coefficients. Two typical examples of the application of the results are given (the analysis of surface layers on oxidized metallic Fe and on tinplate). (Auth.)