In situ and in vivo treatment plan verification and beam monitoring as well as dose control during heavy-ion tumour therapy can be performed in principle by measurements of range distributions of beta(+)-emitting nuclei by means of PET techniques. For this purpose the performance of different types of positron camera as well as the results of in-beam PET experiments using beams of beta(+)-active heavy ions (15O, 17F and 19Ne with energies of 300-500 A MeV) are presented. Following the deduced performance requirements a PET scanner that is designed for clinical use in experimental heavy-ion therapy at GSI Darmstadt has been built. This limited angle tomograph consists of two large-area detector heads based on position sensitive BGO detectors and is predicted to perform the measurement of the end point of a beta(+)-emitting ion beam for the verification of a treatment plan with a precision better than 1 mm. The maximum dose applied in the patient thereby is of the magnitude of 10 mGy.