  A notion of cyclic descents on Dyck paths was introduced by
Adin-Elizalde-Roichman. The cyclic descent set on Dyck path of length $2n$
restricts to the usual descent set when the largest value $2n$ is omitted, and
has the property that the number of Dyck paths with a given cyclic descent set
$D\subset [2n]$ is invariant under cyclic shifts of the entries of $D$. In this
paper, we explicitly describe cyclic descent sets for Motzkin paths. Our
definition provides a constructive combinatorial proof of the existence of
cyclic descent sets, and coincides with that of Adin-Elizalde-Roichman for Dyck
paths.
