Silicone elastomer composites containing multiwalled carbon nanotubes have been irradiated with near-infrared light to study their mechanical actuation response. We show that the speed of the stimulated response is faster than Debye relaxation, instead following a compressed-exponential law. However, the relaxation after switching off the light source follows the simple-exponential relaxation, as does the stimulated response at very low nanotube concentration. We discuss possible models and explanations to account for the fast photomechanical response.