  For discrete autonomous dynamical systems (ADS) $(X, d, f)$, it was found
that in the three conditions defining Devaney chaos, topological transitivity
and dense periodic points together imply sensitive dependence on initial
condition(Banks, Brooks, Cairns, Davis and Stacey, 1992). In this paper, the
result of Banks et al. is generalized to a class of the non-autonomous
dynamical systems (NADS) $(X,f_{1,\infty})$. Also, by the studying of NADS over
their iterated systems $(X,f_{1,\infty}^{[k]})$, we know that for two sensitive
NADS, the one which preserve sensitive in its any times iterated systems is
more sensitive than the one not. In this case, several sufficient conditions
ensuring two kinds of sensitivities are preserved under the arbitrary number of
iterations of certain NADS are given.
