Recently, there has been much interest in the use of neural networks (NNs) in ionospheric prediction models <Williscroft and Poole, 1996; Altinay et al., 1997>. This paper is divided into two parts. The first part presents an extension of the work of Williscroft and Poole <1996>, in which a NN is trained to use nonionospheric geophysical parameters representing time, season, solar cycle, and magnetic activity to estimate foF2. The NN is trained with data from two sunspot cycles at the midlatitude station of Grahamstown (26.5 ¿E, 33.3 ¿S, geographic) and predicts foF2 for various combinations of the input parameters. It is further shown how the squared errors between foF2 estimated from the NN and the measured values are themselves functions of the input parameters, and it is demonstrated how a second NN can be trained to predict the squared error, and hence the rms error, thus providing a measure of the uncertainty in the estimation. These uncertainties lie in the range 0.4--0.9 MHz, a considerable improvement on current non-NN-based models. In the second part, the input data to the net are expanded to include recent measured values of foF2, which leads to a further improvement in the estimation of future values. We conclude that the inclusion of this ionospheric information in the input data is only justified for prediction times up to 4--5 hours ahead, whereafter a knowledge of the most recent values of foF2 does not improve the prediction significantly, and the nonionospheric parameters described in the first part are adequate. ¿ 2000 American Geophysical Union