  We introduce a notion of elliptic differential graded Lie algebra. The class
of elliptic algebras contains such examples as the algebra of differential
forms with values in endomorphisms of a flat vector bundle over a compact
manifold, etc.
  For elliptic differential graded algebra we construct a complete set of
deformations.
  We show that for several deformation problems the existence of a formal power
series solution guarantees the existence of an analytic solution.
