Neural networks are shown to be useful as empirical mathematical models in the calculation of quantitative analytical results, giving sufficient accuracy to compete successfully with various common calibration procedures. The performance of these neural-network models for calibration data from x-ray fluorescence spectrometry (XRF) was evaluated for two training methods, i.e., backward error propagation (BEP) and a genetic algorithm (GA). For a small training set (13 members) of data from Fe/Ni/Cr samples taken from the literature, the BEP-trained models compared favourably with other literature methods. The GA-trained models performed poorly for these samples. The two models performed equally well when trained on a larger data set (30 members) consisting of XRF data for thin Fe/Ni layers on a substrate, for which both the composition and the thickness were determined. The predictive power of both models for samples outside the range of the training set was unsatisfactory.