  Given a Lie group G, one constructs a principal G-bundle on a manifold X by
taking a cover U of X, specifying a transition cocycle on the cover, and
descending the trivialized bundle along the cover. We demonstrate the existence
of an analogous construction for local n-bundles for general n. We establish
analogues for simplicial Lie groups of Moore's results on simplicial groups;
these imply that bundles for strict Lie n-groups arise from local n-bundles.
Our construction leads to simple finite dimensional models of Lie 2-groups such
as String(n).
