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 8e07cf170075e093857e2fac110ee52e" title="Click to view the MathML source">Iν, and the standard estimates for 8e07cf170075e093857e2fac110ee52e" title="Click to view the MathML source">Iν are from a2f4c169ab8b9d78be339" title="Click to view the MathML source">Lp into 83d595453" title="Click to view the MathML source">Lq when bd767a409f221053a0"> and . 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 Is(BMO) when e733edcb49a579b0"> and afcf06" title="Click to view the MathML source">0≤s<ν satisfy a2">. Likewise, we prove estimates for ν -order bilinear fractional integral operators from a2ab6" title="Click to view the MathML source">Lp1×Lp2 into Is(BMO) for various ranges of the indices bde87c643f0155f61d" title="Click to view the MathML source">p1, e79aa63a6786fd8d9bad09b6" title="Click to view the MathML source">p2, and s satisfying .