  We discuss the production of primordial black holes in an early matter
dominated era, which typically takes place in string inspired early universe
cosmological models. In particular, we consider a pre-big bang scenario
(extending previous results regarding formation in the radiation dominated era)
where the enhancement of curvature perturbations is induced by a variation of
the sound-speed parameter c_s during the string phase of high-curvature
inflation. After imposing all relevant observational constraints, we find that
the considered class of models is compatible with the production of a large
amount of primordial black holes, in the mass range relevant to dark matter,
only for a small range of the parameters space. On the other hand, we find that
a huge production of light primordial black holes may occur both in such matter
dominated era and in the radiation dominated one.
