  The classical Dedekind sums appear in the transformation behavior of the
logarithm of the Dedekind eta-function under substitutions from the modular
group. The Dedekind sums and their generalizations are defined in terms of
Bernoulli functions and their generalizations, and are shown to satisfy some
reciprocity relations. In contrast, Dedekind type DC (Daehee and Changhee) sums
and their generalizations are defined in terms of Euler functions and their
generalizations. The purpose of this paper is to introduce the poly-Dedekind
type DC sums, which are obtained from the Dedekind type DC sums by replacing
the Euler function by poly-Euler functions of arbitrary indices, and to show
that those sums satisfy, among other things, a reciprocity relation.
