  In this paper we investigate the iteration problem for several chaos in
non-autonomous discrete system. Firstly, we prove that the Li-Yorke chaos of a
non-autonomous discrete dynamical system is preserved under iterations when
$f_{1,\infty}$ converges to $f$, which weakens the condition in the literature
that $f_{1,\infty}$ uniformly converges to $f$. Besides, we prove that both
DC2' and Kato's chaos of a non-autonomous discrete dynamical system are
iteration invariants. Additionally, we give a sufficient condition for
non-autonomous discrete dynamical system to be Li-Yorke chaos. Finally, we give
an example to show that the DC3 of a non-autonomous discrete dynamical system
is not inherited under iterations, which partly answers an open question
proposed by Wu and Zhu(Chaos in a class of non-autonomous discrete systems,
Appl.Math.Lett. 2013,26:431-436).
