We achieve a classification of n-types of simplicial presheaves in terms of (n-1)-types of presheaves of simplicial groupoids. This can be viewed as a description of the homotopy theory of higher stacks. As a special case we obtain a good homotopy theory of (weak) higher groupoids.
Homology, Homotopy and Applications, Vol. 10 (2008), No. 1, pp.305-325.