In　this　paper,　nilpotent　matrices　over　distributive　lattices　are　considered.　Some　properties　and　characterizations　for　nilpotent　matrices　are　established　and　in　particular,　a　necessary　and　sufficient　condition　for　an　n×n　nilpotent　matrix　to　have　the　nilpotent　index　n　is　given.　Also,　some　properties　of　the　reduction　of　a　nilpotent　matrix　are　obtained.　Partial　results　obtained　in　this　paper　are　results　on　nilpotent　fuzzy　matrices　by　H.　Hashimoto.　©　2004　Elsevier　B.V.　All　rights　reserved.