  We investigate the positivity properties of the direct image
$f_{\ast}(K_{X/Y} \otimes L)$ of the adjoint line bundle associated with a big
and nef line bundle $L$, under a smooth fibration $f: X\to Y$ between
projective varieties. We show that the vector bundle $f_{\ast}(K_{X/Y} \otimes
L)$ is big.
