Functionally　graded　materials　(FGMs)　are　increasingly　being　used　in　high-temperature　structural　components.　The　time-dependent　C-integral,　C(t),　is　a　significant　parameter　in　characterizing　the　crack　tip　stress　field　from　the　small-scale　to　the　extensive　steady-state　creep　stages.　In　this　paper,　the　creep　crack　behavior　of　FGMs　with　a　crack　parallel　to　the　material　property　gradients　was　studied　by　using　the　finite　element　method.　It　was　proven　that　C(t)　remained　valid　for　FGMs.　An　engineering　method　was　proposed　to　estimate　C(t)　in　the　small　scale　and　transition　creep　stages　and　estimate　the　crack　tip　stress　field.　Finite　element　results　verified　that　the　method　could　estimate　C(t)　in　the　small　scale　and　transition　creep　stages　and　estimate　the　crack　tip　stress　field.　For　cases　with　creep　properties　that　increased　in　the　crack　growth　direction,　the　effect　of　constraint　on　the　estimated　crack　tip　stress　field　had　to　be　considered.　The　constraint　parameter　of　Q　was　significantly　affected　by　the　creep　property　gradients.　The　method　was　independent　of　the　gradient　variation　law　of　material　properties.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.