In-beam positron emission tomography (PET) has been proven to be a reliable technique in ion beam radiotherapy for the in situ and non-invasive evaluation of the correct dose deposition in static tumour entities. In the presence of intra-fractional target motion an appropriate time-resolved (four-dimensional, 4D) reconstruction algorithm has to be used to avoid reconstructed activity distributions suffering from motion-related blurring artefacts and to allow for a dedicated dose monitoring. Four-dimensional reconstruction algorithms from diagnostic PET imaging that can properly handle the typically low counting statistics of in-beam PET data have been adapted and optimized for the characteristics of the double-head PET scanner BASTEI installed at GSI Helmholtzzentrum Darmstadt, Germany (GSI). Systematic investigations with moving radioactive sources demonstrate the more effective reduction of motion artefacts by applying a 4D maximum likelihood expectation maximization (MLEM) algorithm instead of the retrospective co-registration of phasewise reconstructed quasi-static activity distributions. Further 4D MLEM results are presented from in-beam PET measurements of irradiated moving phantoms which verify the accessibility of relevant parameters for the dose monitoring of intra-fractionally moving targets. From in-beam PET listmode data sets acquired together with a motion surrogate signal, valuable images can be generated by the 4D MLEM reconstruction for different motion patterns and motion-compensated beam delivery techniques.