  In Ref. [1, 2] a formalism to deal with high-order perturbations of a general
spherical background was developed. In this article, we apply it to the
particular case of a perfect fluid background. We have expressed the
perturbations of the energy-momentum tensor at any order in terms of the
perturbed fluid's pressure, density and velocity. In general, these expressions
are not linear and have sources depending on lower order perturbations. For the
second-order case we make the explicit decomposition of these sources in tensor
spherical harmonics. Then, a general procedure is given to evolve the
perturbative equations of motions of the perfect fluid for any value of the
harmonic label. Finally, with the problem of a spherical collapsing star in
mind, we discuss the high-order perturbative matching conditions across a
timelike surface, in particular the surface separating the perfect fluid
interior from the exterior vacuum.
