  We study the ideal structure of $C^*$-algebras arising from
$C^*$-correspondences. We prove that gauge-invariant ideals of our
$C^*$-algebras are parameterized by certain pairs of ideals of original
$C^*$-algebras. We show that our $C^*$-algebras have a nice property which
should be possessed by generalization of crossed products. Applications to
crossed products by Hilbert $C^*$-bimodules and relative Cuntz-Pimsner algebras
are also discussed.
