This　paper　addresses　periodic　wavelet　bi-frames　associated　with　general　expansive　matrices.　Periodization　is　an　important　method　to　obtain　periodic　wavelets　from　wavelets　on　R-d.　MEP　and　MOEP　provide　us　with　criteria　for　the　construction　of　wavelet　bi-frames　on　R-d.　Based　on　periodization　techniques,　MEP　and　MOEP,　periodic　wavelet　bi-frames　associated　with　the　dyadic　matrix　have　been　constructed.　However,　the　problem　of　constructing　periodic　wavelet　bi-frames　associated　with　general　expansive　matrices　is　still　open.　The　geometry　of　a　general　expansive　matrix　is　much　more　complicated　than　the　dyadic　matrix.　In　this　paper,　with　the　help　of　quasi-norms,　MEP　and　MOEP　we　construct　periodic　wavelet　bi-frames　associated　with　general　expansive　matrices.　(C)　2013　Elsevier　Inc.　All　rights　reserved.