  Talk given at the ``4th Hellenic School on Elementary Particle Physics",
Corfu, 2-20 September 1992: The propagation of strings in cosmological
space-time backgrounds is reviewed. We show the relation of a special class of
cosmological backgrounds to exact conformal field theory. Particular emphasis
is put on the singularity structure of the cosmological space-time and on the
discrete duality symmetries of the string background.
