  A vertex transitive graph $\Gamma$ is said to be $2$-distance transitive if
for each vertex $u$, the group of automorphisms of $\Gamma$ fixing the vertex
$u$ acts transitively on the set of vertices at distance $1$ and $2$ from $u$,
while $\Gamma$ is said to be $2$-arc transitive if its automorphism group is
transitive on the set of $2$-arcs. Then $2$-arc transitive graphs are
$2$-distance transitive. The classification of $2$-arc transitive Cayley graphs
on dihedral groups was given by Du, Malni\v{c} and Maru\v{s}i\v{c} in
[Classification of 2-arc-transitive dihedrants, J. Combin. Theory Ser. B 98
(2008), 1349--1372]. In this paper, it is shown that a connected 2-distance
transitive Cayley graph on the dihedral group of order $2n$ is either $2$-arc
transitive, or isomorphic to the complete multipartite graph $K_{m[b]}$ for
some $m\geq3$ and $b\geq2$ with $mb=2n$.
