  We investigate in a relativistic Hartree theory the gross properties of 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 respective phase spaces are
strongly modified. This results in additional binding of the systems with
distinctively softer equations of state compared to the field free cases. For
magnetic field $\sim 10^{20}$ Gauss and beyond, the nuclear matter in beta
equilibrium practically converts into a stable proton rich matter.
