In　this　paper,　we　obtain　large　deviations　(necessary　and　sufficient　conditions)　of　random　sets　which　take　values　of　bounded　closed　convex　sets　on　the　underling　separable　Banach　space　with　respect　to　the　Hausdorff　distance　dH.　We　also　give　necessary　and　sufficient　conditions　of　large　deviations　for　random　upper　semicontinuous　functions　whose　values　are　of　bounded　closed　convex　levels　on　the　underling　separable　Banach　space　in　the　sense　of　the　uniform　Hausdorff　distance　dH∞.　The　main　tool　is　the　work　of　Wu　on　the　large　deviations　for　empirical　processes　[16].　©　2010　Springer-Verlag　Berlin　Heidelberg.