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We have studied the influences of isospin symmetry breaking ofnucleon-nucleon interaction on the various properties of asymmetrical nuclearmatter and $\beta$-stable matter. For asymmetrical nuclear matter, it is foundthat by including this isospin symmetry breaking, the changes of bulkproperties increase by increasing both density and asymmetry parameter.However, these effects on the total energy and equation of state of$\beta$-stable matter are ignorable. For asymmetrical nuclear matter, thevalidity of the empirical parabolic law in the isospin symmetry breaking caseis shown. It is observed that the isospin symmetry breaking of nucleon-nucleoninteraction affects the $\beta$-equilibrium conditions in $\beta$-stablematter.Comment: 9 figures, International Journal of Theoretical Physics, 43 (2004) in  pres

Isospin Symmetry Breaking Effects on the Properties of Asymmetrical Nuclear Matter and -Stable Matter