  We study the effects of peculiar velocities on statistical measures of galaxy
clustering. These effects occur when distances to the galaxies are estimated
from their redshifts. It is assumed that the clustering pattern results from
the gravitational instability of initially Gaussian, small-amplitude
perturbations of a Friedman-Lemaitre cosmological model. Explicit expressions
are given for an arbitrary density parameter \Omega of the model, both when the
cosmological constant, \Lambda, is zero, and when the model is spatially flat,
\Omega + \Lambda/3H^2 =1. We show how to compute the skewness, or third moment
of the density field, in redshift space, and its Fourier space counterpart, the
bispectrum. We rely on a perturbative expansion of particle trajectories in
Lagrangian coordinates. This formalism extends to higher orders the Zel'dovich
first order solution (1970). We show that a physically consistent and
quantitatively accurate analysis of the growth skewness in redshift space can
be obtained from second-order Lagrangian theory. We also study the effects of
spatial smoothing of the evolved density field. We give analytic expressions
for the gravitationally induced skewness as a function of the power spectrum
and of \Omega, for a spherical top-hat and a Gaussian smoothing filter. We
compare our analytical predictions with measurements performed in numerical
simulations, and find good agreement. These results should then prove useful in
analyzing large scale redshift surveys. In particular, our results, in
conjunction with the recent suggestion of Fry (1994), may help to break the
coupling between the bias and the cosmological
