  We prove birational superrigidity of generic Fano fiber spaces $V/{\mathbb
P}^1$, the fibers of which are Fano complete intersections of index 1 and
dimension $M$ in ${\mathbb P}^{M+k}$, provided that $M\geq 2k+1$. The proof
combines the traditional quadratic techniques of the method of maximal
singularities with the linear techniques based on the connectedness principle
of Shokurov and Koll\' ar. Certain related results are also considered.
