2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/186877We discuss the non--linear growth of the kurtosis of the smoothed peculiar velocity field (along an arbitrary direction), in an Einstein--de Sitter universe, induced by Gaussian primordial density fluctuations. Applying the perturbative theory, we show that, for different cosmological models, a departure from the original Gaussian distribution is gravitationally induced only on small scales ($\simlt 20-30$ Mpc). Models with scale--free power spectrum $P(k)\propto k^{\,n}$, with $-1< n \leq 1$, are also considered. When the fluid particles move according to the Zel'dovich approximation the probability distribution of the peculiar velocity field remains unaltered during the evolution.10 pages in Latex (plus 2 figures in a separate file), PD-cosmo/9401Astrophysicstext