  For a language $L$, we consider its cyclic closure, and more generally the
language $C^k(L)$, which consists of all words obtained by partitioning words
from $L$ into $k$ factors and permuting them. We prove that the classes of ET0L
and EDT0L languages are closed under the operators $C^k$. This both sharpens
and generalises Brandst\"adt's result that if $L$ is context-free then $C^k(L)$
is context-sensitive and not context-free in general for $k\geq 3$. We also
show that the cyclic closure of an indexed language is indexed.
