  Let $G$ be a generalized Baumslag-Solitar group and $\mathcal{C}$ be a class
of groups containing at least one non-unit group and closed under taking
subgroups, extensions, and Cartesian products of the form $\prod_{y \in
Y}X_{y}$, where $X, Y \in \mathcal{C}$ and $X_{y}$ is an isomorphic copy of $X$
for every $y \in Y$. We give a criterion for $G$ to be residually a
$\mathcal{C}$-group provided $\mathcal{C}$ consists only of periodic groups. We
also prove that $G$ is residually a torsion-free $\mathcal{C}$-group if
$\mathcal{C}$ contains at least one non-periodic group and is closed under
taking homomorphic images. These statements generalize and strengthen some
known results. Using the first of them, we provide criteria for a GBS-group to
be a) residually nilpotent; b) residually torsion-free nilpotent; c) residually
free.
