  We develop the theory of n-stacks (or more generally Segal n-stacks which are
$\infty$-stacks such that the morphisms are invertible above degree n). This is
done by systematically using the theory of closed model categories (cmc). Our
main results are: a definition of n-stacks in terms of limits, which should be
perfectly general for stacks of any type of objects; several other
characterizations of n-stacks in terms of ``effectivity of descent data'';
construction of the stack associated to an n-prestack; a strictification result
saying that any ``weak'' n-stack is equivalent to a (strict) n-stack; and a
descent result saying that the (n+1)-prestack of n-stacks (on a site) is an
(n+1)-stack. As for other examples, we start from a ``left Quillen presheaf''
of cmc's and introduce the associated Segal 1-prestack. For this situation, we
prove a general descent result, giving sufficient conditions for this prestack
to be a stack. This applies to the case of complexes, saying how complexes of
sheaves of $\Oo$-modules can be glued together via quasi-isomorphisms. This was
the problem that originally motivated us.
