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 Lp into Lq when bd767a409f221053a0"> 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 Is(BMO) when and afcf06" title="Click to view the MathML source">0≤s<ν satisfy . Likewise, we prove estimates for ν -order bilinear fractional integral operators from Lp1×Lp2 into Is(BMO) for various ranges of the indices e8aa964dabde87c643f0155f61d" title="Click to view the MathML source">p1, p2, and s satisfying e88503574a05eb50fa113">.