Dealing with multidimensional problems has been the ÔÔbottle-neckÕÕ for implementing wavenets to process systems engineering. To tackle this problem, a novel multidimensional wavelet (MW) is presented with its rigorously proven approximation theorems. Taking the new wavelet function as the activation function in its hidden units, a new type of wavenet called multidimensional non-orthogonal non-product wavelet-sigmoid basis function neural network (WSBFN) model is proposed for dynamic fault diagnosis. Based on the heuristic learning rules presented by authors, a new set of heuristic learning rules is presented for determining the topology of WSBFNs. The application of the proposed WSBFN is illustrated in detail with a dynamic hydrocracking process. (1998 Elsevier Science Ltd. All rights reserved.