  In this paper we introduce a simplicial analogue of principal bundles with
commutativity structure and their classifying spaces defined for topological
groups. Our construction $\overline W(\tau,K)$ is a variation of the $\overline
W$-construction for simplicial groups. We show that the geometric realization
of our $\overline W(\tau,K)$ is homotopy equivalent to the topological
classifying space $B(\tau,|K|)$ and we study what objects does the simplicial
set $\overline W(\tau,K)$ classify.
