  Complete differential graded Lie algebras appear to be a wonderful tool for
giving nice algebraic models for the rational homotopy type of non-simply
connected spaces. In particular, there is a realization functor of any Lie
algebra as a simplicial set. In a previous work, we considered the particular
case of a complete graded Lie algebra, $L$, concentrated in degree 0 and proved
that its geometric realization is isomorphic to the usual bar construction on
the Malcev group associated to $L$.
  Here we consider the case of a complete differential graded Lie algebra, $L$,
concentrated in degrees 0 and 1. We first establish that $L$ has the structure
of a crossed module and prove that the geometric realization of $L$ is
isomorphic to the simplicial classifying space of this crossed module.
