  We consider strings with the Nambu action as extremal surfaces in a given
space-time, thus, we ignore their back reaction. Especially, we look for
strings sharing one symmetry with the underlying space-time. If this is a
non-null symmetry, the problem of determining the motion of the string can be
dimensionally reduced. We get exact solutions for the following cases: straight
and circle-like strings in a Friedmann background, straight strings in an
anisotropic Kasner background, different types of strings in the metric of a
gravitational wave. The solutions will be discussed.
