  The maximum gap $g(f)$ of a polynomial $f$ is the maximum of the differences
(gaps) between two consecutive exponents that appear in $f$. Let $\Phi_{n}$ and
$\Psi_{n}$ denote the $n$-th cyclotomic and $n$-th inverse cyclotomic
polynomial, respectively. In this paper, we give several lower bounds for
$g(\Phi_{n})$ and $g(\Psi_{n})$, where $n$ is the product of odd primes. We
observe that they are very often exact. We also give an exact expression for
$g(\Psi_{n})$ under a certain condition. Finally we conjecture an exact
expression for $g(\Phi_{n})$ under a certain condition.
