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 94ea2f4c169ab8b9d78be339" title="Click to view the MathML source">Lp into Lq when e6c000b85fd9bd767a409f221053a0"> and e64ccb">. We show that a ν -order linear fractional integral operator can be continuously extended to a bounded operator from 94ea2f4c169ab8b9d78be339" title="Click to view the MathML source">Lp into the Sobolev-BMO space b95ab6851a303e49a0aa16b7b09c57ed" title="Click to view the MathML source">Is(BMO) when b0"> and 8b3339a849ec7e3d09273afcf06" title="Click to view the MathML source">0≤s<ν satisfy . Likewise, we prove estimates for ν -order bilinear fractional integral operators from 8b59b6451ec436a2ab6" title="Click to view the MathML source">Lp1×Lp2 into b95ab6851a303e49a0aa16b7b09c57ed" title="Click to view the MathML source">Is(BMO) for various ranges of the indices p1, p2, and s satisfying .