Neural networks (NNs) have been used to solve many problems associated with geophysics. This paper describes a new application of NNs to determine optimum parameters for the prediction of foF2, as well as the first application of NNs to the prediction of foF2. We have trained several NNs to predict the noon value of foF2 at Grahamstown (33 ¿S, 26 ¿E) using season, solar activity and magnetic activity as input data, taken over one sunspot cycle (1973--1983). Using the criterion that the best indices of solar and magnetic activity are the ones that give the lowest rms error between predicted and measured foF2, we have determined optimum averaging lengths for these indices. Our optimum index for solar activity is a two month running mean of daily sunspot number, in contrast to the value of 1 year recommended by the International Reference Ionosphere (IRI). Our determination for magnetic activity is a running mean of ak of two days. A neural net trained with these optimum indices can predict the daily noon value of foF2 in Grahamstown with an rms error of .95 MHz. The rms error of the monthly average is .48 MHz. ¿ American Geophysical Union 1996