  We introduce two properties: strong R-property and $C(q)$-property,
describing a special way of divergence of nearby trajectories for an abstract
measure preserving system. We show that systems satisfying the strong
R-property are disjoint (in the sense of Furstenberg) with systems satisfying
the $C(q)$-property. Moreover, we show that if $u_t$ is a unipotent flow on
$G/\Gamma$ with $\Gamma$ irreducible, then $u_t$ satisfies the $C(q)$-property
provided that $u_t$ is not of the form $h_t\times\operatorname{id}$, where
$h_t$ is the classical horocycle flow. Finally, we show that the strong
R-property holds for all (smooth) time changes of horocycle flows and
non-trivial time changes of bounded type Heisenberg nilflows.
