This　paper　addresses　the　Hilbert–Schmidt　frame　(HS-frame)　theory.　We　introduce　the　concept　of　generalized　dual　HS-frame　(g-dual　HS-frame)　which　generalizes　that　of　g-dual　frame.　We　prove　that　two　equivalent　HS-frames　form　a　g-dual　HS-frame　pair,　characterize　operators　on　ℓ2　that　transform　a　pair　of　HS-Riesz　bases　into　a　g-dual　HS-frame　pair,　and　present　a　parametric　expression　of　all　g-dual　HS-frames　of　an　arbitrarily　given　HS-frame.　Also　the　perturbation-stability　and　topological　properties　of　g-dual　HS-frames　are　investigated.　Finally,　applying　our　results,　we　not　only　recover　some　known　results　but　also　derive　some　new　results　in　the　classical　Hilbert　space　frame　setting.　©　2024,　The　Author(s),　under　exclusive　licence　to　Springer　Nature　Switzerland　AG.