In policy learning for robotic manipulation tasks, action parameterization can have a major impact on the final performance and sample efficiency of a policy. Unlike highly-dynamic continuous-control tasks, many manipulation tasks can be efficiently performed by a sequence of simple, smooth end-effector motions. Building on this intuition, we present a new class of policies built on top of differentiable Linear Dynamical System (dLDS) units, our differentiable formulation of the classical LDS. Constructing policies using dLDS units yields several advantageous properties, including trajectory coherence across timesteps, stability, and invariance under translation and scaling. Inspired by the sequenced LDS approach proposed by \citet{lds_dixon}, we propose a deep neural-network policy parameterization based on sequenced dLDS units, and we integrate this policy class into standard on-policy reinforcement learning settings. We conduct extensive experiments on Metaworld environments and show a notable improvement in performance and sample efficiency compared to other state-of-the-art algorithms. Additional visualizations and code can be found at \url{https://sites.google.com/view/deep-sequenced-lds}.