  We study pseudoalgebras from the point of view of pseudo-dual of classical
Lie coalgebra structures. We define the notions of Lie H-coalgebra and Lie
pseudo-bialgebra. We obtain the analog of the CYBE, the Manin triples and
Drinfeld's double for Lie pseudo-bialgebras. We also get a natural description
of the annihilation algebra associated to a pseudoalgebra as a convolution
algebra, clarifying this constructions in the theory of pseudoalgebras.
