We consider migration of low-angle tilt boundaries in nanocrystalline and ultrafine-grained composites each consisting of a metallic matrix and nanoscale incoherent inclusions. Within the model, grain boundaries are considered as the walls of edge dislocations that slip in the metallic matrix but cannot penetrate nanoinclusions. Using the two-dimensional dislocation dynamics simulations, we revealed two principle modes of migration of low-angle grain boundaries. In the first mode, migrating grain boundaries are retarded by nanoinclusions, and grain boundary migration stops. In the second regime, some segments of the migrating grain boundaries are retarded by inclusions while others proceed to migrate by large distances. The transition from the first mode to the second one occurs when the resolved shear stress reaches some critical stress τc. The critical stress increases with increasing the volume fraction of inclusions, while an increase in the distance between the initial position of the migrating grain boundary and the nearest nanoinclusions can either reduce or increase the critical stress.