  In this work, we propose the N=2 and N=4 supersymmetric extensions of the
Lorentz-breaking Abelian Chern-Simons term. We formulate the question of the
Lorentz violation in 6 and 10 dimensions to obtain the bosonic sectors of
$N=2-$ and $N=4-$ supersymmetries, respectively. From this, we carry out an
analysis in N=1, D=4 superspace and, in terms of $N=1-$ superfields, we are
able to write down the N=2 and N=4 supersymmetric extensions of the
Lorentz-violating action term.
