Theoretical equations for fluorescent count rates from bulks, single-layer films, and multiple-layer film specimens, based on fundamental parameter models, are developed. Absorption and secondary enhancement within each layer, between layers, and between layers and substrate are considered. A computer program is used to predict count rates as well as for simultaneous back-calculation of concentrations and thicknesses. Standards can be bulks, single films, or multiple films in any combination; pure-element standards as well as those containing additional elements are suitable. Evaluation of experimental data from two- and three-layer films (by using bulk pure-element standards) by the proposed method shows agreement with <0.3%(absolute) for concentrations and <5%(relative) for thicknesses compared to results from single-layer reference specimens prepared under identical conditions. © 1986.