Inside supernovae neutrinos can undergo resonant spin-flavour oscillations for a wide range of parameters. I will be discussing the conditions for these oscillations. In particular I will be studying the impact of the metallicity of the progenitor on the neutrino signal from a supernova. This is particularly relevant for the well-studied neutrino signal from SN 1987 A. For this event a maximum-likelihood analysis will be presented from which a cautious upper bound on the neutrino magnetic moment can be deduced.