  We present a Lorentz-breaking supersymmetric algebra characterized by a
critical exponent $z$. Such construction requires a non trivial modification of
the supercharges and superderivatives. The improvement of renormalizability for
supersymmetric scalar QED is shown and the K\"ahlerian effective potentials are
calculated in different cases. We also show how the theory flows naturally to
the Lorentz symmetric case at low energies.
