  We study the dynamics of an infinite system of point particles of two types.
They perform random jumps in $\mathbf{R}^d$ in the course of which particles of
different types repel each other whereas those of the same type do not
interact. The states of the system are probability measures on the
corresponding configuration space, the global (in time) evolution of which is
constructed by means of correlation functions. It is proved that for each
initial sub-Poissonian state $\mu_0$, the states evolve $\mu_0 \mapsto \mu_t$
in such a way that $\mu_t$ is sub-Poissonian for all $t>0$. The mesoscopic
(approximate) description of the evolution of states is also given. The
stability of translation invariant stationary states is studied. In particular,
we show that some of such states can be unstable with respect to
space-dependent perturbations.
