Free products of two residually finite groups with amalgamated retracts are considered. It is proved that a cyclic subgroup of such a group is not finitely separable if, and only if, it is conjugated with a subgroup of a free factor which is not finitely separable in this factor. A similar result is obtained for the case of separability in the class of finite p-groups. 2000 Mathematics Subject Classification: primary 20E26, 20E06; secondary 20E22 Keywords: cyclic subgroup separability, residual finiteness, residual p-finiteness, generalized free product, split extension † Corresponding author. Algebra Colloq. 2010.17:577-582. Downloaded from www.worldscientific.com by CHINESE UNIVERSITY OF HONG KONG on 02/18/15. For personal use only.