During radiotherapy treatments of thoracic and abdominal tumors, tumor motion due to respiration has to be considered. Tracking based delivery systems can follow the tumor in real time and therefore enable more precise treatments. One of the problems of such systems is that monitoring the tumor and then reacting to its movement takes a certain amount of time i.e. there is an overall system latency. In this thesis, approaches to cope with system latencies are investigated. Two approaches are considered: a) correlation between external and internal motion, as external observations can be made with virtually no latency and b) motion prediction where a position estimate in the future can be derived from past observations. In systems with very high latencies, comprised of x-ray imaging latencies and response latencies of the beam positioning system, both external-internal correlation as well as prediction has to be integrated. The external-internal correlation models of two commercially available systems, the MHI vero4DRT and the Cyberknife®/SynchronyTM system, were investigated and compared to each other. A predictor was implemented based on Extended Kalman Filtering with a local dynamic model, which is motivated by the elliptic shape of respiratory motion in a plane augmented with time-delayed axes. The prediction and correlation methods were combined in a C++ algorithm. The algorithm performance was evaluated on corresponding tumor and chest motion traces measured on 8 patients at the Mitsubishi RTRT in combination with the AZ 733V Anzai medical belt. The data was simulated for a realistic choice of system parameters, hence 2s imaging- and 100ms beam positioning latency. It was shown that the average root-mean-squared-error of the estimated tumor position over all patients is 1.25mm for an average 12.3mm tumor motion amplitude. The developed algorithm is not capable of compensating circular tumor movement, which results in slightly higher errors in patients showing such characteristics. As an extension of this project, it would be interesting to include circular motion compensation in the algorithm.