  We compare different nonlinear approximations to gravitational clustering in
the weakly nonlinear regime, using as a comparative statistic the evolution of
non-Gaussianity which can be characterised by a set of numbers $S_p$ describing
connected moments of the density field at the lowest order in $<\delta^2>$:
$<\delta^n>_c \simeq S_n<\delta^2>^{n-1}$. Generalizing earlier work by
Bernardeau (1992) we develop an ansatz to evaluate all $S_p$ in a given
approximation by means of a generating function which can be shown to satisfy
the equations of motion of a homogeneous spherical density enhancement in that
approximation. On the basis of the values of we show that approximations
formulated in Lagrangian space (such as the Zeldovich approximation and its
extensions) are considerably more accurate than those formulated in Eulerian
space such as the Frozen Flow and Linear Potential approximations. In
particular we find that the $n$th order Lagrangian perturbation approximation
correctly reproduces the first $n+1$ parameters $S_n$. We also evaluate the
density probability distribution function for the different approximations in
the quasi-linear regime and compare our results with an exact analytic
treatment in the case of the Zeldovich approximation.
