Sea Beam and magnetic surveys of the young (<1 Ma) rise flank around nontransform rise crest offsets at 5.5 ¿N 4.9 ¿N, 3.4 ¿N, 2.0 ¿N, and 2.8 ¿S mapped distinctive trails of obliquely lineated, highly magnetic crust that spreads from the characteristically curving overlapping rift zones. A Deep Tow survey around the small (1.5 km) 3.9 ¿N offset found only normal rise flank terrain. Near-bottom Deep Tow observations at the medium size (9 km) 5.5 ¿N offset and the large (27 km) 2.0 ¿N offset provided more detailed information on the formation of crust in the offset trails, and of the structure of tectonically modified crust at interrift rise crest sites. Patches of interrift crust, which forms deep overlap basins at medium size offsets and basins and plateaus of rotated abyssal hills at large offsets, are periodically shed from the axial zone, together with abandoned portions of overlapped rift zone, to become important elements of the rise flank trails. The oblique azimuths of the paired ''fracture zone'' trails that diverge from the rise crest offsets show that most have migrated along the rise crest at average speeds of 25--125 mm/yr. Net movement of the 27-km 2.8 ¿S offset has been slower, with alternating periods of rapid northward and southward migration. Information on the migration history of the surveyed offsets was supplemented by inferring the migration direction of another eight offsets on the equatorial East Pacific Rise (EPR) whose trails were less than thoroughly mapped. Most offsets of the southern Pacific-Cocos boundary have migrated south, and most on the northern Pacific-Nazca boundary have migrated north; the patterns are not readily explained by the inferred distribution of mantle upwellings along the EPR axis. ¿ American Geophysical Union 1989