  The notion of a generalized Lie bialgebroid (a generalization of the notion
of a Lie bialgebroid) is introduced in such a way that a Jacobi manifold has
associated a canonical generalized Lie bialgebroid. As a kind of converse, we
prove that a Jacobi structure can be defined on the base space of a generalized
Lie bialgebroid. We also show that it is possible to construct a Lie
bialgebroid from a generalized Lie bialgebroid and, as a consequence, we deduce
a duality theorem. Finally, some special classes of generalized Lie
bialgebroids are considered: triangular generalized Lie bialgebroids and
generalized Lie bialgebras.
