  We discuss several PT-symmetric deformations of superderivatives. Based on
these various possibilities, we propose new families of complex PT-symmetric
deformations of the supersymmetric Korteweg-de Vries equation. Some of these
new models are mere fermionic extensions of the former in the sense that they
are formulated in terms of superspace valued superfields containing bosonic and
fermionic fields, breaking however the supersymmetry invariance. Nonetheless,
we also find extensions, which may be viewed as new supersymmetric Korteweg-de
Vries equation. Moreover, we show that these deformations allow for a
non-Hermitian Hamiltonian formulation and construct three charges associated to
the corresponding flow.
