  I show that the standard picture of the neutron star core containing
coexisting neutron and proton superfluids, with the proton component forming a
type II superconductor threaded by flux tubes, is inconsistent with
observations of long-period (~1 yr) precession in isolated pulsars. I conclude
that either the two superfluids coexist nowhere in the stellar core, or the
core is a type I superconductor rather than type II. Either possibility would
have interesting implications for neutron star cooling and theories of spin
jumps (glitches).
