In　this　paper,　we　shall　present　representation　theorems　of　set-valued　martingales　and　set-valued　processes　of　finite　variation　with　continuous　time.　We　shall　also　obtain　a　representation　theorem　of　a　predictable　set-valued　stochastic　process.　We　shall　give　a　new　definition　of　Ito　integral　of　a　set-valued　stochastic　process　with　respect　to　a　Brownian　motion　based　on　the　work　[E.J.　Jung,　J.H.　Kim,　On　set-valued　stochastic　integrals,　Stochastic　Anal.　Appl.　21(2)　(2003)　401-418.].　We　shall　also　discuss　some　properties　of　set-valued　Ito　integral,　especially　the　presentation　theorem　of　set-valued　Ito　integral.　Finally,　we　extend　some　of　above　results　to　the　fuzzy　set-valued　case.　(C)　2006　Published　by　Elsevier　B.V.