For　refinable　function-based　affine　bi-frames,　nonhomogeneous　ones　admit　fast　algorithms　and　have　extension　principles　as　homogeneous　ones.　But　all　extension　principles　are　based　on　some　restrictions　on　refinable　functions.　So　it　is　natural　to　ask　what　are　expected　from　general　refinable　functions.　In　this　paper,　we　introduce　the　notion　of　weak　nonhomogeneous　affine　bi-frame　(WNABF).　Under　the　setting　of　reducing　subspaces　of　L-2　(R-d),　we　characterize　WNABFs　and　obtain　a　mixed　oblique　extension　principle　for　WNABFs　based　on　general　refinable　functions.