  We extend the Falceto-Zambon version of Marsden-Ratiu Poisson reduction to
Poisson quasi-Nijenhuis structures with background on manifolds. We define
gauge transformations of Poisson quasi-Nijenhuis structures with background,
study some of their properties and show that they are compatible with reduction
procedure. We use gauge transformations to construct Poisson quasi-Nijenhuis
structures with background.
