  We study Big-Bang or -Crunch cosmological singularities in 2-dimensional
dilaton-gravity-scalar theories, in general obtained by dimensional reduction
of higher dimensional theories. The dilaton potential encodes information about
the asymptotic data defining the theories, and encompasses various families
such as flat space, $AdS$, conformally $AdS$ as arising from nonconformal
branes, and more general nonrelativistic theories. We find a kind of universal
near singularity behaviour independent of the dilaton potential, giving
universal interrelations between the exponents defining the time behaviour near
the cosmological singularity. More detailed analysis using a scaling ansatz
enables finding various classes of cosmological backgrounds, recovering known
examples such as the $AdS$ Kasner singularity as well finding as new ones. We
give some comments on the dual field theory from this point of view.
