**MSC:**- 05C65 Hypergraphs

${\cal H}(P)$ whose vertices are the elements of $P$ and whose

edges are the maximal intervals of $P$. It is known that ${\cal

H}(P)$ has the K\"{o}nig and dual K\"{o}nig properties for the

class of series-parallel posets. Here we introduce a new class

which contains series-parallel posets and for which the dual

K\"{o}nig property is satisfied. For the class of {\large N}-free

posets, again a generalization of series-parallel posets, we give

a counterexample to see that the K\"{o}nig property is not

satisfied.