On the conjugacy separability of some free constructions of groups by root classes of finite groups

Let C be an arbitrary class of groups which has the root property, consists of finite groups only, and contains at least one nonidentity group. It is proved that every extension of a free group by a C-group is conjugacy C-separable. It is also proved that, if G is a free product of two conjugacy C-separable groups with finite amalgamated subgroup or an HNN-extension of a conjugacy C-separable group with finite associated subgroups, then the group G is residually C if and only if it is conjugacy C-separable.