  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.
