  In a system where selective Mott localization is realized, some electrons
show a gap to charge excitations while others do not. A hybridization between
these two kind of electrons will lead to a smoothening of this sharp difference
and can even bring the system back to a complete delocalization. We show here
that there is a large region of parameters at finite hybridization where the
selective localization persists and the system shows a partial filling of the
selective gap with incoherent states, giving rise to a pseudogap. This result
is illustrated here in a two orbital Hubbard model with Hund's coupling, but is
based on quite general assumptions and should hold for a larger class of
systems, and possibly be a paradigm for the pseudogap mechanism in cuprates.
