We consider non(anti)commutative superspace with coordinate-dependent deformation parameters C^αβ . We show that a chiral N = 1/2 supersymmetry can be defined and that chiral and antichiral superfields are still closed under the Moyal-Weyl associative product implementing the deformation. A consistent N = 1/2 super Yang-Mills deformed theory can be constructed provided C^αβ satisfies a suitable condition which can be connected with the graviphoton background at the origin of the deformation. After adding matter, we also discuss the Konishi anomaly and the gluino condensation.Facultad de Ciencias Exactas