  We study the complexity of constraint satisfaction problems for templates
$\Gamma$ that are first-order definable in $(\Bbb Z; succ)$, the integers with
the successor relation. Assuming a widely believed conjecture from finite
domain constraint satisfaction (we require the tractability conjecture by
Bulatov, Jeavons and Krokhin in the special case of transitive finite
templates), we provide a full classification for the case that Gamma is locally
finite (i.e., the Gaifman graph of $\Gamma$ has finite degree). We show that
one of the following is true: The structure Gamma is homomorphically equivalent
to a structure with a d-modular maximum or minimum polymorphism and
$\mathrm{CSP}(\Gamma)$ can be solved in polynomial time, or $\Gamma$ is
homomorphically equivalent to a finite transitive structure, or
$\mathrm{CSP}(\Gamma)$ is NP-complete.
