  We discuss cosmic Nielsen-Olesen strings in space-times endowed with a
positive cosmological constant. For the cylindrically symmetric, static free
cosmic string, we discuss the contribution of the cosmological constant to the
angle deficit, and to the motion of the null/timelike geodesics. For a
non-gravitating cosmic string in a Schwarzschild-de Sitter space-time, we
discuss how a thin string can pierce the two horizons. We also present a metric
which describes the exterior of a self gravitating thin string present in the
Schwarzschild-de Sitter space-time.
