Abstract An MR-Linac can provide motion information of tumour and organs-at-risk before, during, and after beam delivery. However, MR imaging cannot provide real-time high-quality volumetric images which capture breath-to-breath variability of respiratory motion. Surrogate-driven motion models relate the motion of the internal anatomy to surrogate signals, thus can estimate the 3D internal motion from these signals. Internal surrogate signals based on patient anatomy can be extracted from 2D cine-MR images, which can be acquired on an MR-Linac during treatment, to build and drive motion models. In this paper we investigate different MRI-derived surrogate signals, including signals generated by applying principal component analysis to the image intensities, or control point displacements derived from deformable registration of the 2D cine-MR images. We assessed the suitability of the signals to build models that can estimate the motion of the internal anatomy, including sliding motion and breath-to-breath variability. We quantitatively evaluated the models by estimating the 2D motion in sagittal and coronal slices of 8 lung cancer patients, and comparing them to motion measurements obtained from image registration. For sagittal slices, using the first and second principal components on the control point displacements as surrogate signals resulted in the highest model accuracy, with a mean error over patients around 0.80 mm which was lower than the in-plane resolution. For coronal slices, all investigated signals except the skin signal produced mean errors over patients around 1 mm. These results demonstrate that surrogate signals derived from 2D cine-MR images, including those generated by applying principal component analysis to the image intensities or control point displacements, can accurately model the motion of the internal anatomy within a single sagittal or coronal slice. This implies the signals should also be suitable for modelling the 3D respiratory motion of the internal anatomy.