  We consider two-particle dispersion in a velocity field, where the relative
two-point velocity scales according to $v^{2}(r)\propto r^{\alpha}$ and the
corresponding correlation time scales as $\tau (r)\propto r^{\beta}$, and fix
$\alpha =2/3$, as typical for turbulent flows. We show that two generic types
of dispersion behavior arize: For $\alpha /2+\beta < 1$ the correlations in
relative velocities decouple and the diffusion approximation holds. In the
opposite case, $\alpha /2+\beta >1$, the relative motion is strongly
correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric
situation.
