In　the　realm　of　multiprocessor　systems,　the　evaluation　of　interconnection　network　reliability　holds　utmost　significance,　both　in　terms　of　design　and　maintenance.　The　intricate　nature　of　these　systems　calls　for　a　systematic　assessment　of　reliability　metrics,　among　which,　two　metrics　emerge　as　vital:　connectivity　and　diagnosability.　The　Rg-conditional　connectivity　is　the　minimum　number　of　processors　whose　deletion　will　disconnect　the　multiprocessor　system　and　every　processor　has　at　least　g　fault-free　neighbors.　The　Rg-conditional　diagnosability　is　a　novel　generalized　conditional　diagnosability,　which　is　the　maximum　number　of　faulty　processors　that　can　be　identified　under　the　condition　that　every　processor　has　no　less　than　g　fault-free　neighbors.　In　this　paper,　we　first　investigate　the　Rg-conditional　connectivity　of　generalized　exchanged　X-cubes　GEX(s,t)　and　present　the　lower　(upper)　bounds　of　the　Rg-conditional　diagnosability　of　GEX(s,t)　under　the　PMC　model.　Applying　our　results,　the　Rg-conditional　connectivity　and　the　lower　(upper)　bounds　of　Rg-conditional　diagnosability　of　generalized　exchanged　hypercubes,　generalized　exchanged　crossed　cubes,　and　locally　generalized　exchanged　twisted　cubes　under　the　PMC　model　are　determined.　Our　comparative　analysis　highlights　the　superiority　of　Rg-conditional　diagnosability,　showcasing　its　effectiveness　in　guiding　reliability　studies　across　a　diverse　set　of　networks.　©　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature　2024.