This　paper　addresses　duality　relations　in　HS-frame　theory.　By　introducing　the　notion　of　HS-R-dual　sequence,　some　duality　relations　and　related　results　are　obtained.　We　prove　that　a　sequence　is　an　HS-frame　(HS-frame　sequence,　HS-Riesz　basis)　if　and　only　if　its　HS-R-dual　sequence　is　an　HS-Riesz　sequence　(HS-frame　sequence,　HS-Riesz　basis)　and　characterize　the　(unitary)　equivalence　between　two　HS-frames　in　terms　of　their　HS-R-duals　and　transition　matrices,　respectively.　We　characterize　HS-R-duals　and　prove　that,　given　an　HS-frame,　among　all　its　dual　HS-frames,　only　the　canonical　dual　admits　minimal-norm　HS-R-dual.　And　using　HS-R-duals,　we　also　characterize　dual　HS-frame　pairs.　©　2020　John　Wiley　&　Sons,　Ltd.