Neural networks provide a new tool for the fast solution of repetitive nonlinear curve fitting problems. In this article we introduce the concept of a neural network, and we show how such networks can be used for fitting functional forms to experimental data. The neural network algorithm is typically much faster than conventional iterative approaches. In addition, further substantial improvements in speed can be obtained by using special purpose hardware implementations of the network, thus making the technique suitable for use in fast real-time applications. The basic concepts are illustrated using a simple example from fusion research, involving the .determination of spectral line parameters from measurements of B IV impurity radiation in the COMPASS-C tokamak.