We　give　central　limit　theorems　for　generalized　set-valued　random　variables　whose　level　sets　are　compact　both　in　R-d　or　in　a　Banach　space　under　milder　conditions　than　those　obtained　recently　by　the　latter　two　authors.　(C)　2003　Elsevier　Inc.　All　rights　reserved.