  Dendric subshifts are defined by combinatorial restrictions of the extensions
of the words in its language. This family generalizes well-known families of
subshifts such as Sturmian subshifts, Arnoux-Rauzy subshifts and codings of
interval exchange transformations. It is known that any minimal dendric
subshifts has a primitive $S$-adic representation where the morphisms in $S$
are positive tame automorphisms of the free group generated by the alphabet. In
this paper we investigate those $S$-adic representations, heading towards an
$S$-adic characterization ot this family. We obtain such a characterization in
the ternary case, involving a directed graph with 9 vertices.
