  For a family of geometric objects in the plane
$\mathcal{F}=\{S_1,\ldots,S_n\}$, define $\chi(\mathcal{F})$ as the least
integer $\ell$ such that the elements of $\mathcal{F}$ can be colored with
$\ell$ colors, in such a way that any two intersecting objects have distinct
colors. When $\mathcal{F}$ is a set of pseudo-disks that may only intersect on
their boundaries, and such that any point of the plane is contained in at most
$k$ pseudo-disks, it can be proven that $\chi(\mathcal{F})\le 3k/2 + o(k)$
since the problem is equivalent to cyclic coloring of plane graphs. In this
paper, we study the same problem when pseudo-disks are replaced by a family
$\mathcal{F}$ of pseudo-segments (a.k.a. strings) that do not cross. In other
words, any two strings of $\mathcal{F}$ are only allowed to "touch" each other.
Such a family is said to be $k$-touching if no point of the plane is contained
in more than $k$ elements of $\mathcal{F}$. We give bounds on
$\chi(\mathcal{F})$ as a function of $k$, and in particular we show that
$k$-touching segments can be colored with $k+5$ colors. This partially answers
a question of Hlin\v{e}n\'y (1998) on the chromatic number of contact systems
of strings.
