Federated　learning　(FL)　is　a　distributed　machine　learning　paradigm　that　needs　collaboration　between　a　server　and　a　series　of　clients　with　decentralized　data.　To　make　FL　effective　in　real-world　applications,　existing　work　devotes　to　improving　the　modeling　of　decentralized　non-IID　data.　In　non-IID　settings,　there　are　intra-client　inconsistency　that　comes　from　the　imbalanced　data　modeling,　and　inter-client　inconsistency　among　heterogeneous　client　distributions,　which　not　only　hinders　sufficient　representation　of　the　minority　data,　but　also　brings　discrepant　model　deviations.　However,　previous　work　overlooks　to　tackle　the　above　two　coupling　inconsistencies　together.　In　this　work,　we　propose　FedRANE,　which　consists　of　two　main　modules,　i.e.,　local　relational　augmentation　(LRA)　and　global　Nash　equilibrium　(GNE),　to　resolve　intra-and　inter-client　inconsistency　simultaneously.　Specifically,　in　each　client,　LRA　mines　the　similarity　relations　among　different　data　samples　and　enhances　the　minority　sample　representations　with　their　neighbors　using　attentive　message　passing.　In　server,　GNE　reaches　an　agreement　among　inconsistent　and　discrepant　model　deviations　from　clients　to　server,　which　encourages　the　global　model　to　update　in　the　direction　of　global　optimum　without　breaking　down　the　clients＇　optimization　toward　their　local　optimums.　We　conduct　extensive　experiments　on　four　benchmark　datasets　to　show　the　superiority　of　FedRANE　in　enhancing　the　performance　of　FL　with　non-IID　data.　©　2023　ACM.