For the definitions of cutset, disjoint family and Menger family as well as a statement of Menger's theorem see the review above (Zbl 0678.06001). In this paper it is shown that if an ordered set P contains at most k pairwise disjoint maximal chains, where k is finite, then every finite family of maximal chains in P has a cutset of size at most k. This leads to the following Menger-type result that, if in addition P contains k pairwise disjoint complete maximal chains, then the whole family, M(P), of maximal chains in P has a cutset of size k. A direct proof of this result is also given. The authors then disprove a conjecture by Zaguia by providing an example that shows that the finiteness of k is essential.