Since　a　frame　for　a　Hilbert　space　must　be　a　Bessel　sequence,　many　results　on　(quasi-)affine　bi-frame　are　established　under　the　premise　that　the　corresponding　(quasi-)affine　systems　are　Bessel　sequences.　However,　it　is　very　technical　to　construct　a　(quasi-)affine　Bessel　sequence.　Motivated　by　this　observation,　in　this　paper　we　introduce　the　notion　of　weak　(quasi-)affine　bi-frame　(W(Q)ABF)　in　a　general　reducing　subspace　for　which　the　Bessel　sequence　hypothesis　is　not　needed.　We　obtain　a　characterization　of　WABF,　and　prove　the　equivalence　between　WABF　and　WQABF　under　a　mild　condition.　This　characterization　is　used　to　recover　some　related　known　results　in　the　literature.