Let \(P\) be a partially ordered set every interval of which contains a finite maximal chain. The author poses the problem when the poset \((\text{Int } P, \subseteq)\) of all intervals in \(P\) is selfdual. Let \(U\), \(V\) be equivalence relations on \(P\) with the properties: (i) if \(a\in P\) then \([a] U=\langle u_ 1, v_ 1\rangle\), \([a] V=\langle u_ 2, v_ 2\rangle\) for some \(u_ 1, u_ 2\in \text{Min } P\), \(v_ 1, v_ 2\in \text{Max } P\), (ii) \(U\cap V= \text{id}_ P\), (iii) if \(a,b\in P\), \(a\leq b\), then there exist \(z_ 1, z_ 2\in \langle a,b \rangle\) with \(aU z_ 1 Vb\), \(aV z_ 2 Ub\). The following is proved: (1) If there exist equivalence relations \(U\), \(V\) on \(P\) satisfying (i), (ii), (iii), then there exists a dual automorphism of \((\text{Int } P, \subseteq)\) (which is constructed with the help of \(U\), \(V\)). (2) If \(\Psi\) is a dual automorphism of \((\text{Int } P, \subseteq)\), then there exist equivalence relations, \(U\), \(V\) on \(P\) satisfying (i), (ii), (iii) and an automorphism \(\phi\) of \(P\) such that \(\Psi (\langle a,b\rangle)= \varphi (\langle \phi(a), \phi(b) \rangle)\) where \(\varphi\) is the dual automorphism of \((\text{Int } P, \subseteq)\) corresponding to \(U\), \(V\).