We investigate in a relativistic Hartree theory the gross properties o
f cold symmetric nuclear matter and nuclear matter in beta equilibrium
under the influence of strong magnetic fields. If the field strengths
are above the critical values for electrons and protons, the respecti
ve phase spaces are strongly modified. This results in additional bind
ing of the systems with distinctively softer equations of state compar
ed to the field free cases. For magnetic field approximate to 10(20) G
and beyond, the nuclear matter in beta equilibrium practically conver
ts into a stable proton-rich matter.