Presents a class of high-order neural networks called shunting inhibitory artificial neural networks (SIANNs) for classification and function approximation tasks. In these networks, the basic synaptic interaction is of the shunting inhibitory type. Due to the nonlinearity mediated by shunting inhibition, these networks are capable of producing classifiers with complex nonlinear decision boundaries, ranging from simple hyperplanes to very complex nonlinear surfaces. Therefore, developing efficient training algorithms for these networks will simplify the design of very powerful classifiers and function approximators. In this paper, we present a training method for a feedforward SIANN based on the backpropagation algorithm and on gradient descent.