This paper is concerned with modeling and prediction of lung tumor motion for a new adaptive tumor tracking system in radiotherapy. Information of the tumor motion is used to control a robotic treatment couch, which moves in six degrees of freedom and maintains the tumor in a certain fixed spatial position. With this new technology it is possible to avoid gating during the radiotherapy as well as active breathing control, such that duration and cost of the therapy as well as trauma of the patient can be reduced. The tumor position is detected by an electronic portal imaging device (EPID) such that internal markers for the tumor tracking are no longer necessary. An infrared (IR) camera is introduced to detect abdominal motion, which provides a reference to the respiratory signal and can be used to predict the tumor position over a complete breathing period. This paper presents the effort of tumor motion modeling and prediction. Main challenges with the proposed method in this context are: lack of breathing control causes irregular respiration, low data rate of the EPID device delivers too few information about the tumor position. Two methods, namely an adaptive filtering and a nonlinear method based on Takens Theorem, have been investigated and compared with respect to diverse criteria including prediction accuracy, model complexity and computational effort. Performance analysis with clinical data has shown that both methods can well describe correlation between the EPID and the IR signals, while the adaptive filter possesses advantage with respect of computational effort.