  We extend the definition of the Nijenhuis torsion of an endomorphism of a Lie
algebroid to that of a relation, and we prove that the torsion of the relation
defined by a bi-Hamiltonian structure vanishes. Following Gelfand and Dorfman,
we then define Dirac pairs, and we analyze the relationship of this general
notion with the various kinds of compatible structures on manifolds, more
generally on Lie algebroids.
