  A result of Bridson, Howie, Miller and Short states that if $S$ is a subgroup
of type $FP_{n}(\mathbb{Q})$ of the direct product of $n$ limit groups over
free groups, then $S$ is virtually the direct product of limit groups over free
groups. Furthermore, they characterise finitely presented residually free
groups. In this paper these results are generalised to limit groups over Droms
right-angled Artin groups. Droms RAAGs are the right-angled Artin groups with
the property that all of their finitely generated subgroups are again RAAGs. In
addition, we show that the generalised conjugacy problem is solvable for
finitely presented groups that are residually a Droms RAAG and that their
finitely presentable subgroups are separable.
