An artificial neural network with back-propagation architecture has been applied to the problem of the quantitative analysis of simulated clay mixtures from synthetic X-ray diffraction (XRD) data. A "clay characterization function" (CCF) has been devised that combines information from two clay XRD peaks into a single peak that simplifies the problem which the neural network must solve. In addition, it eliminates peaks from non-layered minerals. A neural network with 17 neurons in the hidden layer and log-sigmoid transfer functions in each layer is sufficiently successful at predicting the compositions of binary and ternary mixtures of the three model clays to demonstrate the potential of the method. Moreover, training is accomplished in relatively short times using a Levenberg-Marquardt algorithm. Although the problem "solved" by this neural network is rather simple, the approach has the potential for the much more complex problem of the quantitative phase analysis of mixtures of real clay minerals. In this study, only the CCF peak heights have been used, but the positions and peak widths also contain important information. It may be practical to include as variables not only the concentrations of clay phases, but also compositional information to which XRD is sensitive.