In　this　paper,　we　study　interval-valued　stochastic　processes　and　stochastic　integrals　with　respect　to　real-valued　Brownian　motion.　Especially　for　interval-valued　martingale　we　obtain　several　equivalent　propositions　based　on　measurable　selections.　By　using　Castaing　representation　of　set-valued　random　variables　we　prove　that　an　intervalvalued　integral　may　be　not　an　interval-valued　martingale　but　an　interval-valued　submartingale,　which　is　different　from　single　valued　stochastic　integrals.　©　2007　IEEE.