We have evaluated photoionization cross sections of H-2 and D-2 with emphasis in resonant effects through intermediate doubly excited states. The theoretical method describes consistently the interference between resonant and nonresonant ionization processes, and includes both dissociative and nondissociative channels. We show that resonant peaks are rather apparent in vibrationally resolved spectra associated to the (1) Sigma(u)(+) symmetry. In contrast,no resonant structure is observed in the total photoionization spectra, in agreement with recent experimental findings. Finally, we show that the ratios of dissociated to undissociated photoions strongly depend on resonant effects. (C) 1997 American Institute of Physics. [S0021-9606(97)00844-1].