Slow, stable shear of granular materials in landslides, beneath glaciers, and along fault surfaces is common, despite little or no intrinsic strengthening of such materials with increasing deformation rate. Compacted, water-saturated sediments, subjected to constant stresses in a ring-shear device, sheared slowly without unstable acceleration in repeated episodes that included pore dilation during shear, attendant pore-water-pressure decline, and consequent strengthening, followed by gradual pore-pressure recovery and weakening. Time-averaged shear velocities (2–800 mm/d) depended inversely on the magnitude of pore dilation with shear and were significantly lower for fine-grained sediment than for coarse-grained sediment, owing to different rates of pore-pressure diffusion in the two materials. When sediment had dilated to its critical-state (steady) porosity and therefore could not dilate further, shear accelerated catastrophically. These data indicate that pore-pressure decreases and consequent strengthening caused by shear-induced dilation may not only suppress rapid shear of landslide debris, subglacial till, and fault gouge, but may also result in slow episodic shear at rates that depend on both material porosity and hydraulic diffusivity.