  The redshift-space correlation function $\xi_s$ for projected galaxy
separations $\simless 1h^{-1}$ Mpc can be expressed as the convolution of the
real-space correlation function with the galaxy pairwise velocity distribution
function (PVDF). An exponential PVDF yields the best fit to the $\xi_s$
measured from galaxy samples of different redshift surveys. We show that this
exponential PVDF is not merely a fitting function but arises from well defined
gravitational processes. Two ingredients conspire to yield a PVDF with a nearly
exponential shape: (i) the number density $n(\sigma)$ of systems with velocity
dispersion $\sigma$; (ii) the unrelaxed dynamical state of most galaxy systems.
The former ingredient determines the exponential tail and the latter the
central peak of the PVDF. We compare the $\xi_s$ measured on non-linear scales
from galaxy samples of the CfA redshift surveys with different models of the
PVDF convolved with the measured real-space correlation function. This
preliminary comparison indicates that the agreement between model and
observations depends strongly on both the underlying cosmological model and the
internal dynamics of galaxy systems. Neither parameter dominates. Moreover, the
agreement depends sensitively on the accuracy of the galaxy position and
velocity measurements.
