The ionospheric critical frequency, f0F2, is forecast 1 hour in advance by using artificial neural networks. The value of f0F2 at the time instant k of the day is designated by f(k). The inputs used for the neural network are the time of day; the day of year; season information; past observations of f0F2; the first difference Δ1(k)=f(k)-f(k-1); the second difference Δ2(k)=Δ1(k)-Δ1(k-1); the relative difference RΔ(k)=Δ1(k)/f(k); geomagnetic indices Kp, ap, Dst, sunspot number, and solar 10.7-cm radio flux; and the solar wind magnetic field components By and Bz. This paper gives a new method, and it is the first application of neural networks for modeling both temporal and spatial dependencies. In order to understand the physical characteristics of the process and determine how important a particular input is, a test which shows the relative significance of inputs to the neural networks is performed at the output. The performance of a neural network is measured by considering errors. For the errors to be more meaningful, training and test times and times for comparison with other results are selected from the same solar activity period. Among the various neural network structures, the best configuration is found to be the one with one hidden layer with five hidden neurons, giving an absolute overall error of 5.88%, or 0.432 MHz. ¿ 1999 American Geophysical Union