We investigate the application of multilayer perception neural networks on the inversion of waveform governing parameters related to the seismic source and the propagation medium. These parameters are given by the size of the source, thicknesses and velocities of the layers, and a parameter &kgr; describing the whole path attenuation of the wave due to absorption. Synthetic SH waves radiated from a circular source model are used for this study. The neural network returns a mapping function which can be used for an entire class of signals, provided that the parameters are within the limits of the model space explored during the training. The application of the mapping function to a set of signals is mathematically simple and fast. This can be a considerable advantage over systematic search techniques, such as simulated annealing or genetic algorithms, since the stability of the results that are found with the neural network can be tested easily with examples not used for the estimation of the mapping function. The use of an appropriate transform of the signal (i.e., spectra or autocorrelation function) gives slightly better results than the crude waveforms. The seismic waveform-governing parameters can be identified with a reasonable accuracy if an appropriate network topology is chosen and if the number of examples used for the training phase is sufficiently large. Even in the case where 16 parameters of the models are searched and the global error remained somewhat unsatisfying, important parameters, such as the source radius or the velocity of the uppermost layers, are still recognized with a fair accuracy. The error is, at least to some degree, an effect of the nonuniqueness of the inversion problem. Performing a search with simulated annealing 31 times for an example seismogram, we obtain 31 solutions with a scatter for the different parameters which is of the same order as the errors obtained with the network. ¿ American Geophysical Union 1996