  In cosmology minisuperspace models are described by nonlinear
time-reparametrization invariant systems with a finite number of degrees of
freedom. Often these models are not explicitly integrable and cannot be
quantized exactly. Having this in mind, we present a scheme for the
(approximate) quantization of perturbed, nonintegrable, time-reparametrization
invariant systems that uses (approximate) gauge invariant quantities. We apply
the scheme to a couple of simple quantum cosmological models.
