A large fraction of known rocky exoplanets are expected to have been spun-down to a state of synchronous rotation, including temperate ones. Studies about the atmospheric and surface processes occurring on such planets thus assume that the day/night sides are fixed with respect to the surface over geological timescales. Here we show that this should not be the case for many synchronous exoplanets. This is due to True Polar Wander (TPW), a well known process occurring on Earth and in the Solar System that can reorient a planet without changing the orientation of its rotational angular momentum with respect to an inertial reference frame. As on Earth, convection in the mantle of rocky exoplanets should continuously distort their inertia tensor, causing reorientation. Moreover, we show that this reorientation is made very efficient by the slower rotation rate of synchronous planets. This is due to the weakness of their combined rotational/tidal bulge---the main stabilizing factor limiting TPW. Stabilization by an elastic lithosphere is also shown to be inefficient. We thus expect the axes of smallest and largest moment of inertia to change continuously over time but to remain closely aligned with the star-planet and orbital axes, respectively.< Leer menos