The author continues her studies of partially ordered semigroups \(S\) which are intraregular, that is, for every \(a\in S\) there are \(x,y\in S\) such that \(a\leq xa^ 2 y\) [see the author, Semigroup Forum 44, 341-346 (1992; Zbl 0756.06008)]. It is shown (similar to the purely semigroup theoretical case) that a p.o. semigroup \((S,\cdot,\leq)\) is intraregular iff \(S\) is a semilattice of simple semigroups. The corresponding semilattice congruence is given by: \(a{\mathcal N} b\) iff \(N(a)=N(b)\), where \(N(a)\) denotes the filter of \(S\) generated by \(a\in S\) [see the author, Semigroup Forum 44, 306-313 (1992; Zbl 0756.06007)]. The special case that \(S/{\mathcal N}\) is a chain with respect to its semilattice-ordering is also characterized: a p.o. semigroup \(S\) is a chain of simple semigroups iff \(S\) is intraregular and the ideals of \(S\) form a chain. Finally, there examples of five-element p.o. semigroups are given which are intraregular and (not) a chain of simple semigroups or not intraregular. (Caution: throughout the paper, ideal \(I\) of \(S\) means a two-sided semigroup-ideal which is at the same time an order-ideal, i.e. \(a\in I\), \(x\in S\), \(x\leq a\) imply \(x\in I\); furthermore, \(S\) simple means that the only ideal --- in this sense --- is \(S\) itself).