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The performance and in-beam imaging capabilities of two position-sensitive γ-ray detectors consisting of Hamamatsu avalanche photodiode arrays (S8550) individually coupled to crystals of cerium-doped lutetium oxyorthosilicate (LSO) are presented. The two detectors were operated in coincidence at the medical beam line of the Gesellschaft für Schwerionenforschung, in Darmstadt, Germany. In a first set of experiments, their imaging performance was tested before, during, and after the irradiation of phantoms of polymethylmethacrylate with carbon ion beams with fluences equivalent to 1000 typical daily therapeutic fractions. Only minor energy, time, and spatial resolution deterioration was observed, with the initial values being recovered after stopping the irradiation. A second set of experiments successfully imaged the depth distribution of positron emitter radionuclides created in a phantom that stopped the high-energy carbon ion beam. The particular details for the in-beam PET acquisition are shortly outlined. The obtained results show that LSO is a suitable material for in-beam PET and that its coupling with avalanche photodiode arrays is feasible for a PET system dedicated to in-beam monitoring of ion therapy.