  Nuclear effective interactions are often modelled by simple analytical
expressions such as the Skyrme zero-range force. This effective interaction
depends on a limited number of parameters that are usually fitted using
experimental data obtained from doubly magic nuclei. It was recently shown that
many Skyrme functionals lead to the appearance of instabilities, in particular
when symmetries are broken, for example unphysical polarization of odd-even or
rotating nuclei. In this article, we show how the formalism of the linear
response in infinite nuclear matter can be used to predict and avoid the
regions of parameters that are responsible for these unphysical instabilities.
