In　this　paper,　we　establish　some　determinantal　inequalities　concerning　M-matrices　and　inverse　M-matrices.　The　main　results　are　as　follows:1.If　A　=　(aij)　is　either　an　n　×　n　M-matrix　or　inverse　M-matrix,　then　for　any　permutation　i1,　i2,　...,　in　of　{1,　2,　...,　n},(a){Mathematical　expression}(b)det　A　=　∏i　=　1n　aii　if　and　only　if　A　is　essentially　triangular.2.If　A　=　(aij)　is　an　n　×　n　M-matrix,　B　=　(bij)　is　an　n　×　n　inverse　M-matrix,　A　{ring　operator}　B　denotes　the　Hadamard　product　of　A　and　B,　then　A　{ring　operator}　B　is　an　M-matrix,　and　for　any　permutation　i1,　i2,　...,　in　of　{1,　2,　...,　n},{Mathematical　expression}.　©　2007　Elsevier　Inc.　All　rights　reserved.