A large intraplate, normal-faulting earthquake (Mw = 7.5) occurred in 1999 in the subducting Cocos plate below the downdip edge of the ruptured thrust fault of the 1978 Oaxaca, Mexico, earthquake (Mw = 7.8). This situation is similar to the previous case of the 1997 normal-faulting event (Mw = 7.1) that occurred beneath the rupture area of the 1985 Michoacan, Mexico, earthquake (Mw = 8.1). We investigate the possibility of any stress interactions between the preceding 1978 thrust and the following 1999 normal-faulting earthquakes. For this purpose, we estimate the temporal change of the stress state in the subducting Cocos plate by calculating the slip distribution during the 1978 earthquake through teleseismic waveform inversion, the dynamic rupture process, and the resultant coseismic stress change, together with the postseismic stress variations due to plate convergence and the viscoelastic relaxation process. To do this, we calculate the coseismic and postseismic changes of all stress components in a three-dimensional space, incorporating the subducting slab, the overlying crust and uppermost mantle, and the asthenosphere. For the coseismic stress change we solve elastodynamic equations, incorporating the kinematic fault slip as an observational constraint under appropriate boundary conditions. To estimate postseismic stress accumulations due to plate convergence, a virtual backward slip is imposed to lock the main thrust zone. The effects of viscoelastic stress relaxations of the coseismic change and the back slip are also included. The maximum coseismic increase in the shear stress and the Coulomb failure stress below the downdip edge of the 1978 thrust fault is estimated to be in the range between 0.5 and 1.5 MPa, and the 1999 normal-faulting earthquake was found to take place in this zone of stress increase. The postseismic variations during the 21 years after the 1978 event modify the magnitude and patterns of the coseismic stress change to some extent but are not large enough to overcome the coseismic change. These results suggest that the coseismic stress increase due to the 1978 thrust earthquake may have enhanced the chance of occurrence of the 1999 normal-faulting event in the subducting plate. If this is the case, one of the possible mechanisms could be static fatigue of rock materials around preexisting weak planes involved in the subducting plate, and it is speculated that that one of these planes might have been reactivated and fractured because of stress corrosion cracking under the applied stress there for 21 years.