  A variation of ordered trees, where each rightmost edge might be marked or
not, if it does not lead to an endnode, is investigated. These marked ordered
trees were introduced by E. Deutsch et al.\ to model skew Dyck paths. We study
the number of deepest nodes in such trees. Explicit generating functions are
established and the average number of deepest nodes, which approaches $\frac53$
when the number of nodes gets large. This is to be compared to standard ordered
trees where the average number of deepest nodes approaches $2$.
