We study the effects of the ionizing and dissociating photons produced by Pop III objects on the surrounding intergalactic medium. We find that the typical size of a H_2 photodissociated region is smaller than the mean distance between sources at z=20-30, but larger than the ionized region. This implies that clearing of the intergalactic H_2 occurs before reionization of the universe is complete. In the same redshift range, the soft-UV background in the Lyman- Werner bands, when the intergalactic H and H_2 opacity is included, is found to be J_LW = 10^-28 - 10^-26 erg cm^-2 s^-1 Hz^-1. This value is well below the treshold required for the negative feedback of Pop III objects on the subsequent galaxy formation to be effective. We have combined these semi-analytical results with high-resolution N-body simulations, to study the topological structure of photoionization and photodissociation and the evolution of the H^+ and H_2 filling factor.
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