When Palisades diabase and Westerly granite are made dilatant by cyclic differential stress not exceeding ~ = 85% of fracture strength, they behave as nonelastic; energy-absorbing media. However, in some ways, their properties show reversibility more typical of elastic media. The quasi-elastic behavior is characterized by the property ''memory.'' Memory in dilatant rock is manifested by the closure of material property hysteresis loops when the sample is returned to certain previous differential stress states. Simple examples of memory have been observed before in Westerly granite. The present work confirms the existence of memory for strain and compressional wave velocity in Westerly granite and Palisades diabase at confining pressures between 250 and 1500 bars. Memory of maxima or minima of the stress difference can be developed, with multiple points remembered simultaneously. A theory of memory based on reversible tensile Griffith cracks was developed which predicts a variety of phenomena, many of which have been observed. A property that is not predicted is the healing which occurs when unloading is stopped and the load is held constant. A time-dependent increase in velocity and decrease in sample volume is observed, consistent with the healing of cracks. Relaxation ceases after approximately 2 min. After relaxation, a further decrease in load produces an initial elastic response followed by a return to the previous nonelastic behavior. Perfect memory is lost when microfracturing occurs as a result of either exceeding the previous absolute maximum stress or extensive cycling. Acoustic emissions are observed for conditions where memory is not perfect and are not observed when memory is perfect. Using travel time data, a new, low value was found for the dependence of dilatancy onset on pressure.