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For a group $G$ that is a limit group over Droms RAAGs such that $G$ hastrivial center, we show that $\Sigma^1(G) = \emptyset = \Sigma^1(G,\mathbb{Q})$. For a group $H$ that is a finitely presented residually DromsRAAG we calculate $\Sigma^1(H)$ and $\Sigma^2(H)_{dis}$. In addition, we obtaina necessary condition for $[\chi]$ to belong to $\Sigma^n(H)$.

On the Bieri-Neumann-Strebel-Renz invariants and limit groups over Droms RAAGs