Summary: The aim of this paper is to evaluate two theorems for the generalized fractional integration of arbitrary complex order involving the product of extended generalized hypergeometric function and a general class of multivariable polynomials. The considered generalized fractional integration operators contain the Appell function as a kernel and are introduced by Saigo and Maeda. The operators studied in this paper generalize the classical Riemann-Liouville, Weyl, Erdélyi-Kober and Saigo operators. Some interesting special cases of our main results are also considered.