Results of a lithospheric stretching model of mid-ocean ridges suggest that the axial valley topography created at active slow-spreading centers may be preserved for tens of millions of years after cessation of spreading. We simulate the evolution of a slow-spreading center using a finite-element model that incorporates a temperature-dependent rheology and discrete faulting. Model results show that significant valley morphology persists after regional extension ceases because the high lithospheric viscosities associated with a slow-spreading center prevent ductile relaxation and because no effective mechanism exists to reverse rift-bounding normal faults. Removal of the axial valley can only be accomplished by reversal of the regional extensional strains immediately upon cessation of active spreading. However, such a process does not seem likely. These results suggest that the persistence of axial valleys at extinct spreading centers is consistent with a lithospheric stretching model for active slow-spreading ridges.