  Non-linear electrodynamics arising in the frames of field theories in
noncommutative space-time is examined on the base of quaternion formalism. The
problem of form-invariance of the corresponding nonlinear constitutive
relations governed by six noncommutativity parameters $\theta_{kl}$ or
quaternion \underline{K} = \underline{\theta} - i \underline{\epsilon} is
explored in detail. Two Abelian 2-parametric small groups, SO(2) \otimes O(1.1)
or T_{2}, depending on invariant length \underline{K}^{2}\neq 0 or
\underline{K}^{2}= 0 respectively, have been found. The way to interpret both
small groups in physical terms consists in factorizing corresponding Lorentz
transformations into Euclidean rotations and Lorentzian boosts. In the context
of general study of various dual symmetries in noncommutative field theory, it
is demonstrated explicitly that the nonlinear constitutive equations under
consideration are not invariant under continuous dual rotations, instead only
invariance under discrete dual transformation exists.
