  Composite hadronic states exhibit interesting properties in the presence of
very intense magnetic fields, such as those conjectured to exist in the
vicinity of certain astrophysical objects. We discuss three scenarios. (i) The
presence of vector particles with anomalous magnetic moment couplings to scalar
particles, induces an instability of the vacuum. (ii) A delicate interplay
between the anomalous magnetic moments of the proton and neutron makes, in
magnetic fields $B\ge 2\times 10^{14}$ T, the neutron stable and for fields
$B\ge 5\times 10^{14}$ T the proton becomes unstable to a decay into a neutron
via $\beta$ emission. (iii) In the unbroken chiral $\sigma$ model magnetic
fields would be screened out as in a superconductor. It is the explicit
breaking of chiral invariance that restores standard electrodynamics.
Astrophysical consequences of all these phenomena are discussed.
