  The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest
integer $p$ such that vertices of $G$ can be partitioned into disjoint classes
$X_{1}, ..., X_{p}$ where vertices in $X_{i}$ have pairwise distance greater
than $i$. For $k < t$ we study the packing chromatic number of infinite
distance graphs $D(k, t)$, i.e. graphs with the set $\Z$ of integers as vertex
set and in which two distinct vertices $i, j \in \Z$ are adjacent if and only
if $|i - j| \in \{k, t\}$.
  We generalize results by Ekstein et al. for graphs $D (1, t)$. For
sufficiently large $t$ we prove that $\chi_{\rho}(D(k, t)) \leq 30$ for both
$k$, $t$ odd, and that $\chi_{\rho}(D(k, t)) \leq 56$ for exactly one of $k$,
$t$ odd. We also give some upper and lower bounds for $\chi_{\rho}(D(k, t))$
with small $k$ and $t$.
  Keywords: distance graph; packing coloring; packing chromatic number
