Trough is an interesting phenomenon in characterizing the behavior of the ionosphere, especially during disturbed conditions. The subject, which was introduced around the 1970s, is still attracting attention, especially during recent years. In HF communication, in particular, over the midlatitude ionospheric regions the electron density trough exhibits a phenomenon of abrupt gradients of electron densities in space and time which are directly reflected to f0F2. Thus the performances of HF communications are directly affected. In this work an attempt has been made for the modeling to quantify the influence of the ionospheric midlatitude electron density trough on the ionospheric critical frequency f0F2 by using neural networks. Data sets are used from the ground stations that include observations in the trough region. It has been demonstrated that the neural-net-based approaches are promising in modeling of the ionospheric processes. Data generated by using statistical relationships are used to train the neural network. Then the trained neural network is used to forecast the ionospheric critical frequency, f0F2, values 1 hour in advance for the cases when the probability of influence of the trough is high. Preliminary results will be presented to discuss the suitability of the neural-network-based approach in the modeling of complex processes such as the influence of the trough on f0F2. The basic contributions of this work are 1) generation and organization of significant data for teaching complex processes, 2) neural-network-based modeling of a highly complex nonlinear process such as the influence of the trough on f0F2 forecasting, and 3) general demonstration of learning capability by calculating cross correlations and general demonstration of reaching a proper operating point by calculating errors (that is, during the optimization process the neural network reaches the global minimum by using the gradient descent method). ¿ 2001 American Geophysical Union