  A cohomology for product systems of Hilbert bimodules is defined via the Ext
functor. For the class of product systems corresponding to irreversible
algebraic dynamics, relevant resolutions are found explicitly and it is shown
how the underlying product system can be twisted by the 2-cocycles. In
particular, this process gives rise to cohomological deformations of the
C*-algebras associated with the product system. Concrete examples of
deformations of the Cuntz's algebra Q_N arising this way are investigated and
we show they are simple and purely infinite.
