  In this talk we review briefly the basic features of non-critical
(dissipative) String Cosmologies, and we confront some of these models with
supernova data. We pay particular attention to the off-shell and dilaton
contributions to the dynamical evolution equations of the non-critical string
Universe, as well as the Boltzmann equation for species abundances. The latter
could have important consequences for the modification of astrophysical
constraints on physically appealing particle physics models, such as
supersymmetry. The data fits show that non-critical string cosmologies may be
viable alternatives to LambdaCDM model.
