Birational geometry of varieties fibred into complete intersections of codimension two

In this paper we prove the birational superrigidity of Fano-Mori fibre spaces pi: V -> S all of whose fibres are complete intersections of type d(1) . d(2) in the projective space P-d1+(d2) satisfying certain conditions of general position, under the assumption that the fibration V/S is sufficiently twisted over the base (in particular, under the assumption that the K-condition holds). The condition of general position for every fibre guarantees that the global log canonical threshold is equal to one. This condition also bounds the dimension of the base S by a constant depending only on the dimension M of the fibre (this constant grows like M-2/2 as M -> infinity). The fibres and the variety V may have quadratic and bi-quadratic singularities whose rank is bounded below.