The use of feedforward neural networks for process modeling has proven very successful for steady-state applications, but suitable applications for dynamic systems are still being studied. A novel approach is presented in this paper which uses intrinsically dynamic neurons inspired from biological control systems as the processing elements in network architectures. This results in a network which incorporates dynamic elements with continuous feedback. Two case studies show that the recurrent dynamic neuron network (RDNN) does an excellent job of predicting nonlinearities such as asymmetric dynamic response. In addition, the RDNN significantly outperforms linear models and more traditional neural network models for open-loop simulations. Finally it is shown how this RDNN model can be used in model-based control architectures, such as internal model control.