This paper presents precise relative relocations for aftershocks of 59 intermediate and deep earthquakes, using P, pP, and PKP arrival times read by us or reported in the literature. These aftershocks included 36 ''rupture subevents,'' occurring within 1 min of the initial event, and 71 ''true aftershocks,'' occurring later and identified statistically as being related to the initial event. We compare the relative locations with the orientations of the Wadati-Benioff zones and with the available focal mechanisms using statistical methods not previously applied to earthquake data. Surprisingly, neither true aftershocks nor rupture subevents cluster along the nodal planes of intermediate or deep earthquake focal mechanisms. Aftershocks more than 20 km from the initial events occur preferentially in the plane of the Wadati-Benioff zone, while those lying closer have isotropically distributed directions. Rupture subevents occur after the travel time of the S wave from the initial event. Larger-magnitude earthquakes generally possess rupture subevents lying farther from the inital event, whereas true aftershocks can occur 50 km or more from initial events having magnitudes as small as 5.3. Except following a few unusually large earthquakes with focal depths of about 100 km, we find no rupture subevents or true aftershocks more than 80 km from the initial hypocenter. The existence of many aftershocks far from nodal planes does not favor models in which deep earthquake failure is simply slip along a planar fault. Rather, the aftershocks may occur in response to a general redistribution of stress caused either by the occurrence of the initial event or, possibly, by nearby continuing phase transition. Alternatively, the failure zones of deep earthquakes may be surfaces which are frequently curved by 40¿ or more from the orientation of the intial nodal plane, perhaps due to inhomogeneous stress distributions. ¿ American Geophysical Union 1987