  We present a method to construct a basis of singular and non-singular common
eigenvectors for Gaudin Hamiltonians in a tensor product module of the Lie
algebra SL(2). The subset of singular vectors is completely described by
analogy with covariant differential operators. The relation between singular
eigenvectors and the Bethe Ansatz is discussed. In each weight subspace the set
of singular eigenvectors is completed to a basis, by a family of non-singular
eigenvectors. We discuss also the generalization of this method to the case of
an arbitrary Lie algebra.
