The　convergence　of　the　power　sequence　of　an　n×n　fuzzy　matrix　has　been　studied.　Some　theoretical　necessary　and　sufficient　conditions　have　been　established　for　the　power　sequence　to　be　convergent　generally.　Furthermore,　as　one　of　our　main　concerns,　the　convergence　index　was　studied　in　detail,　especially　for　some　special　types　of　Boolean　matrices.　Also　it　has　been　established　that　the　convergence　index　is　bounded　by　(n-1)2+1　from　above　for　an　arbitrary　n　×　n　fuzzy　matrix　if　its　power　sequence　converges.　Our　method　is　concentrated　on　the　limit　behavior　of　the　power　sequence.　It　helped　us　to　make　our　proofs　be　simpler　and　more　direct　than　those　in　pure　algebraic　methods.　©　1997　Korean　Society　of　Computational　&　Applied　Mathematics　and　Korean　SIGCOAM　(Korea　Information　Processing　Society).