In this note we deal with a question concerning monounary algebras which is analogous to an open problem for partially ordered sets proposed by Duffus and Rival.
The aim of the present paper is to describe all connected monounary algebras for which there exists a representation by means of connected monounary algebras which are retract irreducible in the class ${\mathcal U}_c$ (or in ${\mathcal U} $).