In this study we address the problem of predicting the position of a moving lung tumor during respiration on the basis of external breathing signals--a technique used for beam gating, tracking, and other dynamic motion management techniques in radiation therapy. We demonstrate the use of neural network filters to correlate tumor position with external surrogate markers while simultaneously predicting the motion ahead in time, for situations in which neither the breathing pattern nor the correlation between moving anatomical elements is constant in time. One pancreatic cancer patient and two lung cancer patients with mid/upper lobe tumors were fluoroscopically imaged to observe tumor motion synchronously with the movement of external chest markers during free breathing. The external marker position was provided as input to a feed-forward neural network that correlated the marker and tumor movement to predict the tumor position up to 800 ms in advance. The predicted tumor position was compared to its observed position to establish the accuracy with which the filter could dynamically track tumor motion under nonstationary conditions. These results were compared to simplified linear versions of the filter. The two lung cancer patients exhibited complex respiratory behavior in which the correlation between surrogate marker and tumor position changed with each cycle of breathing. By automatically and continuously adjusting its parameters to the observations, the neural network achieved better tracking accuracy than the fixed and adaptive linear filters. Variability and instability in human respiration complicate the task of predicting tumor position from surrogate breathing signals. Our results show that adaptive signal-processing filters can provide more accurate tumor position estimates than simpler stationary filters when presented with nonstationary breathing motion.