Root Class Residuality of HNN-Extensions with Central Cyclic Associated Subgroups

Let $\mathcal{R}$ be a root class of groups which is closed with respect to passage to quotient groups and contains at least one nonidentity group. A criterion for the $\mathcal{R}$-residuality of an HNN-extension whose associated subgroups are cyclic and belong to the center of the base group is obtained.