  String propagation is investigated in de Sitter and black hole backgrounds
using both exact and approximative methods. The circular string evolution in de
Sitter space is discussed in detail with respect to energy and pressure,
mathematical solution and physical interpretation, multi-string solutions etc.
We compare with the circular string evolution in the 2+1 dimensional black hole
anti de Sitter spacetime and in the equatorial plane of ordinary 3+1
dimensional stationary axially symmetric spacetime solutions of Einstein
general relativity. Using an approximative string perturbation approach we
consider also generic string evolution and propagation in all these curved
spacetimes. (To appear in the proceedings of the 2eme Journee Cosmologie held
in Paris, June 1994)
