The self-consistent approach to the magnetic field evolution in neutron star (NS) cores, developed recently, is generalized to the case of superfluid and superconducting NSs. Applying this approach to the cold matter of NS cores composed of neutrons, protons, electrons, and muons, we find that, similarly to the case of normal matter, an arbitrary configuration of the magnetic field may result in generation of macroscopic particle velocities, strongly exceeding their diffusive (relative) velocities. This effect substantially accelerates evolution of the magnetic field in the stellar core. An hierarchy of time-scales of such evolution at different stages of NS life is proposed and discussed. It is argued that the magnetic field in the core cannot be considered as frozen or vanishing and that its temporal evolution should affect the observational properties of NSs.

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