  We study the relation between the Jordan-Einstein frame transition and the
possible description of the crossing of singularities in flat Friedmann
universes, using the fact that the regular evolution in one frame can
correspond to crossing singularities in the other frame. We show that some
interesting effects arise in simple models such as one with a massless scalar
field or another wherein the potential is constant in the Einstein frame. The
dynamics in these models and in their conformally coupled counterparts are
described in detail, and a method for the continuation of such cosmological
evolutions beyond the singularity is developed. We compare our approach with
some other, recently developed, approaches to the problem of the crossing of
singularities.
