  An underlying fundamental assumption in relativistic perturbation theory is
the existence of a parametric family of spacetimes that can be Taylor expanded
around a background. Since the choice of the latter is crucial, sometimes it is
convenient to have a perturbative formalism based on two (or more) parameters.
A good example is the study of rotating stars, where generic perturbations are
constructed on top of an axisymmetric configuration built by using the slow
rotation approximation. Here, we discuss the gauge dependence of non-linear
perturbations depending on two parameters and how to derive explicit higher
order gauge transformation rules.
