  We investigate the properties of the standard perturbative expansions which
describe the early stages of the dynamics of gravitational clustering. We show
that for hierarchical scenarios with no small-scale cutoff perturbation theory
always breaks down beyond a finite order $q_+$. Besides, the degree of
divergence increases with the order of the perturbative terms so that
renormalization procedures cannot be applied. Nevertheless, we explain that
despite the divergence of these subleading terms the results of perturbation
theory are correct at leading order because they can be recovered through a
steepest-descent method which does not use such perturbative expansions.
Finally, we investigate the simpler cases of the Zel'dovich and Burgers
dynamics. In particular, we show that the standard Burgers equation exhibits
similar properties. This analogy suggests that the results of the standard
perturbative expansions are valid up to the order $q_+$ (i.e. until they are
finite). Moreover, the first ``non-regular'' term of a large-scale expansion of
the two-point correlation function should be of the form $R^{-2} \sigma^2(R)$.
At higher orders the large-scale expansion should no longer be over powers of
$\sigma^2$ but over a different combination of powers of 1/R. However, its
calculation requires new non-perturbative methods.
