  Given a GGS-group $G$ with non-constant defining tuple over a prime-regular
rooted tree, we calculate the indices $|G:G^{(n)}|$ and describe the structure
of the higher derived subgroups $G^{(n)}$ for all $n \in \mathbb{N}$. We find
that the values $|G:G^{(n)}|$ depend only mildly on the structure of the
defining tuple.
