  Let $\mathcal{C}$ be a class of groups. A group $X$ is said to be residually
a $\mathcal{C}$-group (conjugacy $\mathcal{C}$-separable) if, for any elements
$x,y \in X$ that are not equal (not conjugate in $X$), there exists a
homomorphism $\sigma$ of $X$ onto a group from $\mathcal{C}$ such that the
elements $x\sigma$ and $y\sigma$ are still not equal (respectively, not
conjugate in $X\sigma$). A generalized Baumslag-Solitar group or GBS-group is
the fundamental group of a finite connected graph of groups whose all vertex
and edge groups are infinite cyclic. An ordinary Baumslag-Solitar group is the
GBS-group that corresponds to a graph containing only one vertex and one loop.
Suppose that the class $\mathcal{C}$ consists of periodic groups and is closed
under taking subgroups and unrestricted wreath products. We prove that a
non-solvable GBS-group is conjugacy $\mathcal{C}$-separable if and only if it
is residually a $\mathcal{C}$-group. We also find a criterion for a solvable
GBS-group to be conjugacy $\mathcal{C}$-separable. As a corollary, we prove
that an arbitrary GBS-group is conjugacy (finite) separable if and only if it
is residually finite.
