  In this paper we set-up a general framework for a formal deformation theory
of Dirac structures. We give a parameterization of formal deformations in terms
of two-forms obeying a cubic equation. The notion of equivalence is discussed
in detail. We show that the obstruction for the construction of deformations
order by order lies in the third Lie algebroid cohomology of the Dirac
structure. However, the classification of inequivalent first order deformations
is not given by the second Lie algebroid cohomology but turns out to be more
complicated.
