Lower lobe lung tumours in particular can move up to 2 cm in the cranio-caudal direction during the respiration cycle. This breathing motion causes image artefacts in conventional free-breathing computed tomography (CT) and positron emission tomography (PET) scanning, rendering delineation of structures for radiotherapy inaccurate. The purpose of this study was to develop a method for four-dimensional (4D) respiration-correlated (RC) acquisition of both CT and PET scans and to develop a framework to fuse these modalities. The breathing signal was acquired using a thermometer in the breathing airflow of the patient. Using this breathing signal, the acquired CT and PET data were grouped to the corresponding respiratory phases, thereby obtaining 4D CT and PET scans. Tumour motion curves were assessed in both image modalities. From these tumour motion curves, the deviation with respect to the mean tumour position was calculated for each phase. The absolute position of the centre of the tumour, relative to the bony anatomy, in the RCCT and gated PET scans was determined. This 4D acquisition and 4D fusion methodology was performed for five patients with lower lobe tumours. The peak-to-peak amplitude range in this sample group was 1-2 cm. The 3D tumour motion curve differed less than 1 mm between PET and CT for all phases. The mean difference in amplitude was less than 1 mm. The position of the centre of the tumour (relative to the bony anatomy) in the RCCT and gated PET scan was similar (difference <1 mm) when no atelectasis was present. Based on these results, we conclude that the method described in this study allows for accurate quantification of tumour motion in CT and PET scans and yields accurate respiration-correlated 4D anatomical and functional information on the tumour region.