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Accurate prediction of tumour motion - over a prescribed time - is essential for enabling adaptive radiotherapy. The prediction time horizon is determined by measurement processing time, predictor algorithm processing time and the time-to-adapt radiation delivery. A trade off between the predictor algorithm complexity and the required prediction time horizon, therefore, has to be made. This paper proposes an interacting multiple model (IMM) filter and two Kalman filters to predict 0.2 s ahead respiratory tumour motions. The performance of the filters is evaluated using 333 traces of 4 minutes respiratory motions for 24 adult patients. The average RMSE of the IMM filter and the best Kalman filter with 5Hz measurements rate are 0.98 mm and 1.1 mm, which are improvements of 38% and 30% compared to use of measurements only.