  The paper is concerned with the equilibrium distribution $\Pi_n$ of the
$n$-th element in a sequence of continuous-time density dependent Markov
processes on the integers. Under a $(2+\a)$-th moment condition on the jump
distributions, we establish a bound of order $O(n^{-(\a+1)/2}\sqrt{\log n})$ on
the difference between the point probabilities of $\Pi_n$ and those of a
translated Poisson distribution with the same variance. Except for the factor
$\sqrt{\log n}$, the result is as good as could be obtained in the simpler
setting of sums of independent integer-valued random variables. Our arguments
are based on the Stein-Chen method and coupling.
