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 e52e" title="Click to view the MathML source">Iν, and the standard estimates for e52e" title="Click to view the MathML source">Iν are from a2f4c169ab8b9d78be339" title="Click to view the MathML source">Lp into a191d1f5b61df2383d595453" title="Click to view the MathML source">Lq when e6c000b85fd9bd767a409f221053a0"> and e64ccb">. We show that a ν -order linear fractional integral operator can be continuously extended to a bounded operator from a2f4c169ab8b9d78be339" title="Click to view the MathML source">Lp into the Sobolev-BMO space a16b7b09c57ed" title="Click to view the MathML source">Is(BMO) when and 0≤s<ν satisfy 82b771c8cf17c2eaa6320d3645a2">. Likewise, we prove estimates for ν -order bilinear fractional integral operators from a2ab6" title="Click to view the MathML source">Lp1×Lp2 into a16b7b09c57ed" title="Click to view the MathML source">Is(BMO) for various ranges of the indices p1, p2, and s satisfying 88503574a05eb50fa113">.