  Consider a pronilpotent DG (differential graded) Lie algebra over a field of
characteristic 0. In the first part of the paper we introduce the reduced
Deligne groupoid associated to this DG Lie algebra. We prove that a DG Lie
quasi-isomorphism between two such algebras induces an equivalence between the
corresponding reduced Deligne groupoids. This extends the famous result of
Goldman- Millson (attributed to Deligne) to the unbounded pronilpotent case.
  In the second part of the paper we consider the Deligne 2-groupoid. We show
it exists under more relaxed assumptions than known before (the DG Lie algebra
is either nilpotent or of quasi quantum type). We prove that a DG Lie
quasi-isomorphism between such DG Lie algebras induces a weak equivalence
between the corresponding Deligne 2-groupoids.
  In the third part of the paper we prove that an L-infinity quasi-isomorphism
between pronilpotent DG Lie algebras induces a bijection between the sets of
gauge equivalence classes of Maurer-Cartan elements. This extends a result of
Kontsevich and others to the pronilpotent case.
