  We discuss chirality-preserving nilpotent deformations of four-dimensional
N=(1,1) Euclidean harmonic superspace and their implications in N=(1,1)
supersymmetric gauge and hypermultiplet theories, basically following
[hep-th/0308012] and [hep-th/0405049]. For the SO(4) x SU(2) invariant
deformation, we present non-anticommutative Euclidean analogs of the N=2 gauge
multiplet and hypermultiplet off-shell actions. As a new result, we consider a
specific non-anticommutative hypermultiplet model with N=(1,0) supersymmetry.
It involves free scalar fields and interacting right-handed spinor fields.
