Fault　diagnostic　analysis　is　extremely　important　for　interconnection　networks.　The　t′/g-diagnosis　imprecise　strategy　plays　an　essential　role　in　the　reliability　of　networks.　The　t′/g-diagnosis　strategy　can　detect　up　to　t′　faulty　vertices　which　might　include　at　most　g　misdiagnosed　vertices.　The　exchanged　hypercube　is　obtained　by　systematically　removing　links　from　a　binary　hypercube,　which　has　smaller　maximum　degree　and　Wiener　index　than　the　hypercube.　We　use　GEH(s,t)　to　denote　the　generalized　exchanged　hypercube,　and　show　in　this　paper　that　GEH(s,t)　is　[(g　+　1)s　-g(g+1)　2　+　1]/g-diagnosable　with　1　≤　s　≤　t　and　0　≤　g　≤　s　-　1　under　the　PMC　model　and　MM∗　model.　We　also　propose　a　t′/g-diagnosis　algorithm　on　GEH(s,t).　As　a　side　benefit,　the　t′/g-diagnosability　of　the　dual-cube-like　network　DCn　can　be　directly　obtained　from　our　results.　©　2021　World　Scientific　Publishing　Company.