  We introduce the notion of interlacing log-concavity of a polynomial sequence
$\{P_m(x)\}_{m\geq 0}$, where $P_m(x)$ is a polynomial of degree m with
positive coefficients $a_{i}(m)$. This sequence of polynomials is said to be
interlacing log-concave if the ratios of consecutive coefficients of $P_m(x)$
interlace the ratios of consecutive coefficients of $P_{m+1}(x)$ for any $m\geq
0$. Interlacing log-concavity is stronger than the log-concavity. We show that
the Boros-Moll polynomials are interlacing log-concave. Furthermore we give a
sufficient condition for interlacing log-concavity which implies that some
classical combinatorial polynomials are interlacing log-concave.
