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 Iν, and the standard estimates for Iν are from Lp into Lq when and . 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 49a0aa16b7b09c57ed" title="Click to view the MathML source">Is(BMO) when 49a579b0"> and 49ec7e3d09273afcf06" 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 49a0aa16b7b09c57ed" title="Click to view the MathML source">Is(BMO) for various ranges of the indices bde87c643f0155f61d" title="Click to view the MathML source">p1, p2, and s satisfying .