  We study the quasilinear evolution of the one-point probability density
functions (PDFs) of the smoothed density and velocity fields in a cosmological
gravitating system beginning with Gaussian initial fluctuations. Our analytic
results are based on the Zel'dovich approximation and laminar flow. A numerical
analysis extends the results into the multistreaming regime using the smoothed
fields of a CDM N-body simulation. We find that the PDF of velocity, both
Lagrangian and Eulerian, remains Gaussian under the laminar Zel'dovich
approximation, and it is almost indistinguishable from Gaussian in the
simulations. The PDF of mass density deviates from a normal distribution early
in the quasilinear regime and it develops a shape remarkably similar to a
lognormal distribution with one parameter, the \rms density fluctuation
$\sigma$. Applying these results to currently available data we find that the
PDFs of the velocity and density fields, as recovered by the \pot\ procedure
from observed velocities assuming $\Omega=1$, or as deduced from a redshift
survey of \iras\ galaxies assuming that galaxies trace mass, are consistent
with Gaussian initial fluctuations.
