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 Lp into Lq when e6c000b85fd9bd767a409f221053a0"> and a472d112f022525becde64ccb">. We show that a ν -order linear fractional integral operator can be continuously extended to a bounded operator from Lp into the Sobolev-BMO space 851a303e49a0aa16b7b09c57ed" title="Click to view the MathML source">Is(BMO) when e733edcb49a579b0"> and 0≤s<ν satisfy 82b771c8cf17c2eaa6320d3645a2">. Likewise, we prove estimates for ν -order bilinear fractional integral operators from Lp1×Lp2 into 851a303e49a0aa16b7b09c57ed" title="Click to view the MathML source">Is(BMO) for various ranges of the indices p1, e79aa63a6786fd8d9bad09b6" title="Click to view the MathML source">p2, and s satisfying 8503574a05eb50fa113">.