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

CMB anisotropies and linear matter power spectrum in models with non-thermal neutrinos and primordial magnetic fields