  We study cosmic Nielsen-Olesen strings in space-times with a positive
cosmological constant. For the free cosmic string in a cylindrically symmetric
space-time, we calculate the contribution of the cosmological constant to the
angle deficit, and to the bending of null geodesics. For a cosmic string in a
Schwarzschild-de Sitter space-time, we use Kruskal patches around the inner and
outer horizons to show that a thin string can pierce them.
