  In this talk we present a field theoretical model constructed in Minkowski
N=1 superspace with a deformed supercoordinate algebra. Our study is motivated
in part by recent results from super-string theory, which show that in a
particular scenario in Euclidean superspace the spinor coordinates \theta do
not anticommute. Field theoretical consequences of this deformation were
studied in a number of articles. We present a way to extend the discussion to
Minkowski space, by assuming non-vanishing anticommutators for both \theta, and
\bar{\theta}. We give a consistent supercoordinate algebra, and a star product
that is real and preserves the (anti)chirality of a product of (anti)chiral
superfields. We also give the Wess-Zumino Lagrangian that gains
Lorentz-invariant corrections due to non(anti)commutativity within our model.
The Lagrangian in Minkowski superspace is also always manifestly Hermitian.
