The　concept　of　R-duals　of　a　sequence　was　first　introduced　with　the　motivation　to　obtain　a　general　version　of　duality　principle　in　Gabor　analysis.　Since　then,　various　R-duals　(types　II,　III,　IV)　and　some　relaxations　of　the　R-dual　setup　have　been　introduced　and　studied　by　some　mathematicians.　All　these　＂R-duals＂　provide　a　powerful　tool　in　the　analysis　of　duality　relations　in　general　frame　theory.　It　is　of　independent　interest　in　mathematics　and　far　beyond　the　duality　principle　in　Gabor　analysis.　Observe　that　the　underlying　sequences　of　a　R-dual　are　a　pair　of　orthonormal　bases.　In　this　paper　we　introduce　the　concept　of　weak　R-duals　based　on　a　pair　of　Parseval　frames.　It　is　a　new　relaxation　of　the　R-dual　setup.　We　obtain　a　characterization　of　frames　based　on　their　weak　R-duals,　and　prove　that　the　weak　R-dual　of　a　frame　(Riesz　basis)　is　a　frame　sequence　(frame).　We　also　characterize　(unitarily)　equivalent　frames　in　terms　of　weak　R-duals.　Finally,　we　present　an　explicit　expression　of　the　canonical　duals　of　weak　R-duals.