A large, nearly vertical, normal-faulting earthquake (Mw = 7.1) took place in 1997 in the subducting Cocos plate just beneath the ruptured fault zone of the 1985 Michoacan, Mexico, earthquake (Mw = 8.1). We investigate the possibility of stress interaction between the two large events through a 3D analysis of coseismic-stress change that was due to the first event, taking into consideration the postseismic change and the dynamic rupture process of the second event. In the middle portion of the subducting plate at depths below 30 km, the calculated coseismic increase in the vertical-shear stress and in the Coulomb-failure stress beneath the high stress-drop zones of the 1985 earthquake is in the order of 0.4 to 0.8 MPa. It was also found that the 1997 earthquake took place in the zone of maximum coseismic-stress increase. Possible postseismic-stress changes due to the subduction process or to the loading of the overriding continental lithosphere and from aseismic slip would enhance the coseismic-stress change and hence the possibility of occurrence of a normal-faulting earthquake in the subducting plate. The dynamic rupture pattern of the 1997 event seems to be consistent with the inferred stress interactions.