  This paper gives some simple estimates of the essential norm for the
difference of composition operators induced by $\phi$ and $\psi$ acting on
bounded function space in the unit polydiscs $U^n$, where $\phi(z)$ and
$\psi(z)$be holomorphic self-maps of $U^n$. As its applications, a
characterization of compact difference is given for composition operators
acting on the bounded function spaces.
