  Let F_0=B,...,F_n be a sequence of differentiable manifolds, G_i a Lie
subgroup of diffeomorphisms of F_i, and H_i a subgroup of G_i central in G_i.
We suppose also given a locally trivial bundle p_{K_i} over F_{i-1} which
typical fiber is K_i the quotient of G_i by H_i. The aim of this paper is to
study the differential geometry of the following problem: classify sequences
M_n\to...M_1, where each map from M_i to M_{i-1} is a locally trivial fibration
which typical fiber is F_i and which transition functions image are elements of
G_i. We associate to this problem a tower of gerbes and define for it the
notion of connective structure, curvature and holonomy using the notion of free
transitive distribution (free TD)
