  Nonlinear approximation methods such as the Zeldovich approximation, and more
recently the frozen flow and linear potential approximations, are sometimes
used to simulate nonlinear gravitational instability in the expanding Universe.
We investigate the relative accuracy of these approximations by comparing them
with the exact solution using second order perturbation theory. We evaluate the
density and velocity fields in these approximations to second order, and also
determine the skewness parameter $S_3 = \langle \delta^3 \rangle / \langle
(\delta^{(1)})^2\rangle ^2$ for each of the approximations again in second
order. We find that $S_3 = 4, ~3, ~3.4$ for the Zeldovich approximation, the
frozen flow and the linear potential approximations respectively as compared to
$S_3 = {34/7}$ for the exact solution. Our results show that, of all the
approximations considered, the Zeldovich approximation is the most accurate in
describing the weakly nonlinear effects of gravity. Moreover, the Zeldovich
approximation is much closer to the exact results for matter and velocity
distributions than the other approximations if the slope of the power spectrum
of density perturbations is $-3< n \le -1$.
