The application of artificial neural networks to dynamical systems has been constrained by the non-dynamical nature popular network architectures. Many of-the difficulties that ensue-large network sizes, long training times, the need to predetermine buffer lengths- can be overcomed with dynamic neural networks. The minimization of a quadratic performance index is considered for trajectory tracking or process simulation applications. Two approaches for gradient computation are discussed: forward and adjoint sensitivity analysis. The computational complexity of the latter is significantly less, but it requires a backward integration capability. We also discuss two parameter updating methods: gradient descent and a Levenberg-Marquardt approach.