  In this paper we construct the Seiberg-Witten maps for superfields on the
theta-theta deformed superspaces with N=(1/2,0) and N=(1/2,1/2) supersymmety.
We show that on the N=(1/2,0) deformed superspace there is no Seiberg-Witten
map for antichiral superfields which is at the same time antichiral, local and
which preserves the N=(1/2,0) supersymmetry. Solutions which break these
requirements are presented. On the N=(1/2,1/2) deformed superspace we show that
for the chiral gauge parameter, and therefore also for the chiral matter field,
there is no chiral Seiberg-Witten map. Some other possible Seiberg-Witten maps
for the superfields are presented.
