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Cancer is one of the leading causes of death worldwide, and head and neck (H&N) cancer is amongst the most prevalent types. Positron emission tomography and computed tomography are used to detect, segment and quantify the tumor region. Clinically, tumor segmentation is extensively time-consuming and prone to error. Machine learning, and deep learning in particular, can assist to automate this process, yielding results as accurate as the results of a clinician. In this paper, we investigate a vision transformer-based method to automatically delineate H&N tumor, and compare its results to leading convolutional neural network (CNN)-based models. We use multi-modal data from CT and PET scans to perform the segmentation task. We show that a solution with a transformer-based model has the potential to achieve comparable results to CNN-based ones. With cross validation, the model achieves a mean dice similarity coefficient (DSC) of 0.736, mean precision of 0.766 and mean recall of 0.766. This is only 0.021 less than the 2020 competition winning model (cross validated in-house) in terms of the DSC score. On the testing set, the model performs similarly, with DSC of 0.736, precision of 0.773, and recall of 0.760, which is only 0.023 lower in DSC than the 2020 competition winning model. This work shows that cancer segmentation via transformer-based models is a promising research area to further explore.