  Let G be a connected reductive group. To any irreducible G-variety one
associates a certain linear group generated by reflections called the Weyl
group. Weyl groups play an important role in the study of embeddings of
homogeneous spaces. We establish algorithms for computing Weyl groups for
homogeneous spaces and affine homogeneous vector bundles. For some special
classes of G-varieties (affine homogeneous vector bundles of maximal rank,
affine homogeneous spaces, homogeneous spaces of maximal rank with discrete
group of central automorphisms) we compute Weyl groups more or less explicitly.
