  In this paper, we define and study generalizations of expansiveness, namely
n- expansiveness, $\aleph_0$-expansiveness, continuum-wise expansive and meagre
expansiveness for non-autonomous discrete dynamical systems. We discuss various
properties of such non-autonomous systems and give necessary examples. We prove
results related to non-existence of $\aleph_0$-expansive and meagre expansive
non-autonomous system on certain spaces. We also study relation between
$\aleph_0$-expansive and meagre-expansive non-autonomous systems.
