  In this work, we present two possible venues to accomodate the $K_{F}$-type
Lorentz-symmetry violating Electrodynamics in an $N=1$-supersymmetric
framework. A chiral and a vector superfield are chosen to describe the
background that signals Lorentz-symmetry breaking. In each case, the $\ K_{\mu
\nu \kappa \lambda }$-tensor is expressed in terms of the components of the
background superfield that we choose to describe the breaking. We also present
in detail the actions with all fermionic partners of the background that
determine $\ K_{\mu \nu \kappa \lambda }$.
