  In this paper we propose and discuss a mirror construction for complete
intersections in partial flag manifolds $F(n_1, ..., n_l, n)$. This
construction includes our previous mirror construction for complete
intersection in Grassmannians and the mirror construction of Givental for
complete flag manifolds. The key idea of our construction is a degeneration of
$F(n_1, ..., n_l, n)$ to a certain Gorenstein toric Fano variety $P(n_1, ...,
n_l, n)$ which has been investigated by Gonciulea and Lakshmibai. We describe a
natural small crepant desingularization of $P(n_1, ..., n_l, n)$ and prove a
generalized version of a conjecture of Gonciulea and Lakshmibai on the singular
locus of $P(n_1, ..., n_l, n)$.
