In this article, we explore the mapping and boundedness properties of linear and bilinear fractional integral operators acting on Lebesgue spaces with large indices. The prototype ν -order fractional integral operator is the Riesz potential 857e2fac110ee52e" title="Click to view the MathML source">Iν, and the standard estimates for 857e2fac110ee52e" title="Click to view the MathML source">Iν are from 9ab8b9d78be339" title="Click to view the MathML source">Lp into 9a191d1f5b61df2383d595453" title="Click to view the MathML source">Lq when 85fd9bd767a409f221053a0"> and a472d112f022525becde64ccb">. We show that a ν -order linear fractional integral operator can be continuously extended to a bounded operator from 9ab8b9d78be339" title="Click to view the MathML source">Lp into the Sobolev-BMO space 851a303e49a0aa16b7b09c57ed" title="Click to view the MathML source">Is(BMO) when 9a02d03fe733edcb49a579b0"> and 9a849ec7e3d09273afcf06" title="Click to view the MathML source">0≤s<ν satisfy 8182b771c8cf17c2eaa6320d3645a2">. Likewise, we prove estimates for ν -order bilinear fractional integral operators from 81478b59b6451ec436a2ab6" title="Click to view the MathML source">Lp1×Lp2 into 851a303e49a0aa16b7b09c57ed" title="Click to view the MathML source">Is(BMO) for various ranges of the indices e8aa964dabde87c643f0155f61d" title="Click to view the MathML source">p1, e79aa63a6786fd8d9bad09b6" title="Click to view the MathML source">p2, and s satisfying e88503574a05eb50fa113">.