Data from stress-controlled ring-shear experiments indicate that shear deformation of saturated granular materials may be repeatedly stabilized by dilatant hardening. For initially dense, saturated sediments, deformation caused by an externally-controlled decrease in effective stress is suppressed by the decline of pore-water pressure that results from shear-zone dilation. Halting of deformation and dilation allows re-equilibration of pore pressure and results in renewed shear. This process is intrinsic to granular materials that dilate during shear displacement and is capable of self-sustaining cyclicity. These findings have important implications for processes such as slow landsliding, aseismic fault slip, and glacier-bed deformation.