Let ${cal C}$ be a nonempty class of finite groups closed under taking subgroups, homomorphic images and extensions. A subgroup $H$ of an abstract residually ${cal C}$ group $R$ is said to be conjugacy ${cal C}$-distinguished if whenever $yin R$, the
n $y$ has a conjugate in $H$ if and only if the same holds for the images of $y$ and $H$ in every quotient group $R/Nin {cal C}$ of $R$. We prove that in a group having a normal free subgroup $Phi$ such that $R/Phi$ is in ${cal C}$, every finitely generated subgroup is conjugacy ${cal C}$-distinguished. We also prove that finitely generated subgroups of limit groups, of Lyndon groups and certain one-relator groups are conjugacy distinguished (${cal C}$ here is the class of all finite groups).
