Recent findings have shown that the brain’s internal representation of the external world shifts over days, a phenomenon termed representational drift [Driscoll et al., 2017, Rule et al., 2020]. Thus, it becomes crucial to account for such non-stationarities when investigating the roles of circuits in the brain. While linear dynamical system (LDS) models are commonly used to characterize the dynamics of neural population activity, they assume a stable mapping from the latent states to neural activity. This limits their ability to capture non-stationary processes---such as representational drift---in the brain that occur over long timescales. To address this limitation, we introduce Stiefel manifold dynamical system (SMDS) models, a new class of models designed to account for drift in neural representations. In SMDS, the emission matrices are constrained to be orthonormal and evolve smoothly over sessions on the Stiefel manifold---the space of all orthonormal subspaces---while the dynamics parameters are shared across sessions. This allows SMDS to leverage data across sessions while accounting for non-stationarity, and thus capture the underlying neural dynamics more accurately compared to a stationary LDS. Additionally, it provides a measure of representational drift. We show the utility of SMDS using both simulated and real data experiments. First, we simulate non-stationary neural data to show that stationary LDS models infer an incorrect higher-dimensional underlying dynamical system than the true model, while SMDS accurately tracks drift, achieves a higher log likelihood and better reconstruction of held-out data. We then apply SMDS to macaque neural recordings during a reach-and-grasp task [Rouse \& Schieber, 2015], revealing inter-session drift in neural recordings. Our results demonstrate that SMDS provides a powerful framework for capturing representational drift, offering new insights into long-term neural dynamics.