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Abstract In response to external stimuli, such as heat, light, or magnetic fields, stimuli-responsive soft materials can change their current configuration to a new equilibrium state through non-equilibrium kinetic processes, including reaction, diffusion, and viscoelastic relaxation, which generates novel spatiotemporal shape-morphing behavior. Using a photothermal shape memory polymer (SMP) cantilever beam as a model system, this work analytically, numerically, and experimentally studies its non-equilibrium kinetic processes and spatiotemporal bending under light illumination. We establish a thermomechanical model for SMPs capturing the concurrent non-equilibrium processes of heat transfer and viscoelastic relaxation, which induces inhomogeneous temperature and strain distributions through the thickness of the beam, resulting in its bending and unbending. By varying the key dimensionless parameters, we theoretically and experimentally observe different types of bending dynamics. Moreover, our theory takes into consideration changes in the angles of incidence caused by extensive beam bending, and demonstrates that this effect can dramatically delay the bending due to reduction of the effective light intensity, which is further validated experimentally. This work demonstrates programmable and predictable spatiotemporal morphing of SMPs, and provides design guidelines for SMP morphing structures and robots.