  Two quasi-linear approximations, the frozen flow approximation (FFA) and the
frozen potential approximation (FPA), have been proposed recently for studying
the evolution of a collisionless self-gravitating fluid. In the FFA it is
assumed that the velocity field remains unchanged from its value obtained from
the linear theory whereas in FPA the same approximation is made for the
gravitational potential. In this paper we compare these and the older
Zel'dovich approximation by calculating the evolution of the density in
perturbation theory. In particular we compute the skewness, including the
smoothing effects, and the kurtosis for the FFA, FPA and Zel'dovich
approximation and compare their relative accuracy.
