  Starting with assumptions both simple and natural from "physical" point of
view we present a direct construction of transformations preserving wide class
of (anti)commutation relations which describe Euclidean/Minkowski superspace
quantizations. These generalized transformations act on deformed superspaces as
the ordinary ones do on undeformed spaces but they depend on non(anti)commuting
parameters satisfying some consistent (anti)commutation relations. Once the
coalgebraic structure compatible with the algebraic one is introduced in the
set of transformations we deal with quantum symmetry supergroup. This is the
case for intensively studied so called N=1/2 supersymmetry as well as its three
parameter extension. The resulting symmetry transformations - supersymmetric
extension of theta-Euclidean group can be regarded as global counterpart of
appropriately twisted Euclidean superalgebra that has been shown to preserve
N=1/2 supersymmetry.
