  Angular power spectra of temperature anisotropies and polarization of the
cosmic microwave background (CMB) as well as the linear matter power spectra
are calculated for models with three light neutrinos with non-thermal
phase-space distributions in the presence of a primordial stochastic magnetic
field. The non-thermal phase-space distribution function is assumed to be the
sum of a Fermi-Dirac and a gaussian distribution. It is found that the known
effective description of the non-thermal model in terms of a twin thermal model
with extra relativistic degrees of freedom can also be extended to models
including a stochastic magnetic field. Numerical solutions are obtained for a
range of magnetic field parameters.
