  In this paper we consider the iterated Brownian motion $
^{\mu_1}_{\mu_2}\!I(t) = B_1^{\mu_1} ( | B_{2}^{\mu_2} (t)|) $ where
$B_j^{\mu_j} , j=1,2$ are two independent Brownian motions with drift $\mu_j$.
Here we study the last zero crossing of $ ^{\mu_1}_{\mu_2}\!I(t) $ and for this
purpose we derive the last zero-crossing distribution of the drifted Brownian
motion. We derive also the joint distribution of the last zero crossing before
$ t $ and of the first passage time through the zero level of a Brownian motion
with drift $ \mu $ after $ t $. All these results permit us to derive explicit
formulas for ${^I_\mu T_0} = \sup \{ s < \max_{0\leq z\leq t} |B_2(z)| :
B_1^\mu (s) = 0 \}$. Also the iterated zero-crossing $ {^{\mu_1} T}_{0,
{^{\mu_2} T}_{0,t}} $ is analyzed and extended to the case where the level of
nesting is arbitrary.
