  We study the consequences of superconducting quark cores in neutron stars for
the magnetic fields of pulsars. We find that within recent nonperturbative
approaches to the effective quark interaction the diquark condensate forms a
superconductor of second kind whereas previously quark matter was considered as
a first kind superconductor. In both cases the magnetic field which is
generated in the surrounding hadronic shell of superfluid neutrons and
superconducting protons can penetrate into the quark matter core since it is
concentrated in neutron vortices where the field strength exceeds the critical
value. Therefore the magnetic field will not be expelled from the
superconducting quark core with the consequence that there is no decay of the
magnetic fields of pulsars. Thus we conclude that the occurence of a
superconducting quark matter core in pulsars does not contradict the
observational data which indicate that magnetic fields of pulsars have life
times larger than $10^7$ years.
