This　paper　is　devoted　to　studying　the　existence　of　positive　solutions　for　the　following　integral　system　{u(x)　=　integral(Rn　)vertical　bar　x　-　y　vertical　bar(lambda)(　)v(　)(-q)(y)dy,　p,　q　＞　0,　lambda　is　an　element　of　(0,　infinity),　n　＞=　1.　v(x)　=　integral(Rn　)vertical　bar　x　-　y　vertical　bar(lambda)u(-p)(y)dy,　It　is　shown　that　if　(u,　v)　is　a　pair　of　positive　Lebesgue　measurable　solutions　of　this　integral　system,　then　1/p　-　1　+　1/q　-　1　=　lambda/n,　which　is　different　from　the　well-known　case　of　the　Lane-Emden　system　and　its　natural　extension,　the　Hardy-Littlewood-Sobolev　type　integral　equations.