 Quasi-excellent rings are closely related to the problem of resolution of singularities, and this seems to have been Grothendieck's motivation for defining them.Grothendieck (1965) observed that if it is possible to resolve singularities of all complete integral local Noetherian rings, then it is possible to resolve the singularities of all reduced quasi-excellent rings.Hironaka (1964) proved this for all complete integral Noetherian local rings over a field of characteristic 0, which implies his theorem that all singularities of excellent schemes over a field of characteristic 0 can be resolved.