  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 versions of the Lorentz-violating action
term.
