  A variety of gauges are used in cosmological perturbation theory. These are
often chosen in order to attribute physical properties to a particular choice
of coordinates, or otherwise to simplify the form of the resultant equations.
Calculations are then performed with the understanding that they could have
been done in any gauge, and that transformations between different gauges can
be made at will. We show that this logic can be extended to the domain of large
density contrasts, where different types of perturbative expansion are
required, but that the way in which gauges can be chosen in the presence of
such structures is severely constrained. In particular, most gauges that are
commonly considered in the cosmology literature are found to be unviable in the
presence of non-linear structures. This includes spatially flat gauge,
synchronous gauge, comoving orthogonal gauge, total matter gauge, N-body gauge,
and the uniform density gauge. In contrast, we find that the longitudinal gauge
and the Newtonian motion gauge are both viable choices in both standard
cosmological perturbation theory, and in the post-Newtonian perturbative
expansions that are required in order to model non-linear structures.
