  This paper is an extension of an earlier paper that dealt with global
dynamics in autonomous triangular maps. In the current paper, we extend the
results on global dynamics of autonomous triangular maps to periodic
non-autonomous triangular maps. We show that, under certain conditions, the
orbit of every point in a periodic non-autonomous triangular map converges to a
fixed point (respectively, periodic orbit of period $p$) if and only if there
is no periodic orbit of prime period two (respectively, periodic orbits of
prime period greater than $p$).
