The　article　aims　at　discussing　the　Choquet　integrals　of　set-valued　random　variables　with　respect　to　capacities.　We　firstly　state　representation　theorems　and　subadditive　property　of　set-valued　Choquet　integrals.　Then　we　mainly　prove　Fatou＇s　Lemmas,　Lesbesgue　dominated　convergence　theorem　and　monotone　convergence　theorems　of　set-valued　Choquet　integrals　under　the　weaker　conditions　than　that　in　previous　works.　©　2011　Springer-Verlag　Berlin　Heidelberg.