Two-dimensional　hidden　Markov　model　(2-D　HMM)　is　an　extension　of　1-D　HMM　to　2-D,　it　provides　a　reasonable　statistical　method　to　model　matrix　data.　This　paper　presents　some　new　strict　definitions　of　2-D　HMM　and　proves　the　equivalence　between　them,　and　gives　a　study　of　the　three　basic　problems　for　2-D　HMM,　namely,　probability　evaluation,　optimal　state　matrix　and　parameter　estimation.　By　using　the　ideal　that　the　sequences　of　states　on　columns　or　rows　of　a　2-D　HMM　can　be　seen　as　states　of　a　1-D　HMM,　several　new　formulae　solving　these　problems　are　theoretically　derived　and　further　demonstrated　by　computer　simulations.　(c)　2006　Elsevier　Inc.　All　rights　reserved.