  Vanishing results for reduced $L_{p,q}$-cohomology are established in the
case of twisted products, which are a~generalization of warped products. Only
the case $q \leq p$ is considered. This is an extension of some results by
Gol'dshtein, Kuz'minov and Shvedov about the $L_{p}$-cohomology of warped
cylinders. One of the main observations is the vanishing of the
"middle-dimensional" cohomology for a large class of manifolds. This means that
the $L_2$-Betty numbers are zero in the "middle dimension".
