The need for a better representation of traffic dynamics and the reproduction of traffic flow motion on the network have been the main reasons to seek solutions for dynamic network loading (DNL) models. In this paper, a neural network (NN) approximator that supports the DNL model is utilized to model link flow dynamics on a sample network. The presented DNL model is constructed with a linear travel time function for link performances and an algorithm written with a set of rules considering the constraints of link dynamics, flow conservation, flow propagation, and boundary conditions. Each of the three selected NN methods, i.e., feedforward back-propagation NN, radial basis function NN, and generalized regression NN, is utilized in the integrated model structure in order to determine the most appropriate one, and hence, three DNL processes are simulated. Traffic dynamics such as inflow rates, outflow rates, and delays are selected to evaluate the performance of the proposed model.