  The string equations of motion for some homogeneous (Kantowski-Sachs, Bianchi
I and Bianchi IX) background spacetimes are given, and solved explicitly in
some simple cases. This is motivated by the recent developments in string
cosmology, where it has been shown that, under certain circumstances, such
spacetimes appear as string-vacua.
  Both tensile and null strings are considered. Generally, it is much simpler
to solve for the null strings since then we deal with the null geodesic
equations of General Relativity plus some additional constraints.
  We consider in detail an ansatz corresponding to circular strings, and we
discuss the possibility of using an elliptic-shape string ansatz in the case of
homogeneous (but anisotropic) backgrounds.
