Supernova neutrinos can exhibit a rich variety of flavour conversion mechanisms. In particular, current research is dedicated mostly to “fast” self-induced flavor conversions, which can happen almost immediately above the core and can induce flavour equilibration. This effect can have an impact on the shock heating and on the r-process occurring during the explosion. In this talk I discuss a systematic approach to study the instabilities developing in the flavour space, which are causing fast flavour conversions. This approach was originally developed in the context of plasma physics. Representative numerical solutions are discussed in a simple two-beam model of interacting neutrinos.