This paper introduces a new method called Dynamic Node Creation (DNC) which automatically grows BP networks until the target problem is solved. DNC sequentially adds nodes one at a time to the hidden layer(s) of the network until the desired approximation accuracy is achieved. Simulation results for parity, symmetry, binary addition, and the encoder problem are presented. The procedure was capable of finding known minimal topologies in many cases, and was always within three nodes of the minimum. Computational expense for finding the solutions was comparable to training normal BP networks with the same final topologies. Starting out with fewer nodes than needed to solve the problem actually seems to help find a solution. The method yielded a solution for every problem tried.