Purpose: To investigate multiple deep learning methods for automated segmentation (auto-segmentation) of the parotid glands, submandibular glands, and level II and level III lymph nodes on magnetic resonance imaging (MRI). Outlining radiosensitive organs on images used to assist radiation therapy (radiotherapy) of patients with head and neck cancer (HNC) is a time-consuming task, in which variability between observers may directly impact on patient treatment outcomes. Auto-segmentation on computed tomography imaging has been shown to result in significant time reductions and more consistent outlines of the organs at risk. Methods: Three convolutional neural network (CNN)-based auto-segmentation architectures were developed using manual segmentations and T2-weighted MRI images provided from the American Association of Physicists in Medicine (AAPM) radiotherapy MRI auto-contouring (RT-MAC) challenge dataset (n = 31). Auto-segmentation performance was evaluated with segmentation similarity and surface distance metrics on the RT-MAC dataset with institutional manual segmentations (n = 10). The generalizability of the auto-segmentation methods was assessed on an institutional MRI dataset (n = 10). Results: Auto-segmentation performance on the RT-MAC images with institutional segmentations was higher than previously reported MRI methods for the parotid glands (Dice: 0.860 ± 0.067, mean surface distance [MSD]: 1.33 ± 0.40 mm) and the first report of MRI performance for submandibular glands (Dice: 0.830 ± 0.032, MSD: 1.16 ± 0.47 mm). We demonstrate that high-resolution auto-segmentations with improved geometric accuracy can be generated for the parotid and submandibular glands by cascading a localizer CNN and a cropped high-resolution CNN. Improved MSDs were observed between automatic and manual segmentations of the submandibular glands when a low-resolution auto-segmentation was used as prior knowledge in the second-stage CNN. Reduced auto-segmentation performance was observed on our institutional MRI dataset when trained on external RT-MAC images; only the parotid gland auto-segmentations were considered clinically feasible for manual correction (Dice: 0.775 ± 0.105, MSD: 1.20 ± 0.60 mm). Conclusions: This work demonstrates that CNNs are a suitable method to auto-segment the parotid and submandibular glands on MRI images of patients with HNC, and that cascaded CNNs can generate high-resolution segmentations with improved geometric accuracy. Deep learning methods may be suitable for auto-segmentation of the parotid glands on T2-weighted MRI images from different scanners, but further work is required to improve the performance and generalizability of these methods for auto-segmentation of the submandibular glands and lymph nodes.