We have theoretically studied the effect of autoionization through doubly-excited autoionizing states on the photoelectron energy spectrum in (1+2＇)-photon above-threshold ionization (ATI) of H-2 molecules. We have considered excitation from the ground X (1)Sigma(g)(v "=0,j ") state to the dissociation continuum of autoionizing states of (1)Sigma(u) and (1)Pi(u) symmetry, via the intermediate resonant B (1)Sigma(u)(v(＇)=5, j(＇)) state. These autoionizing states decay to form molecular ions in the dissociation continuum (dissociative autoionization) and in the bound vibrational levels (nondissociative autoionization) of the ionic ground state (X (2)Sigma(g)), as well as free electrons carrying extra energy. We have found that the photoelectron spectrum (PES) is mainly determined by the autoionization from the doubly-excited autoionizing states of ungerade symmetry, and that it is oscillatory in nature and shows a structure similar to that observed in a recent experiment by Rottke [J. Phys. B 30, 4049 (1997).] (C) 2000 American Institute of Physics. [S0021-9606(00)00507-9].