  We study quantized equations of motion and currents, that means equations on
the level of Green's functions, in three different approaches to noncommutative
quantum field theories. At first, the case of only spatial noncommutativity is
investigated in which the modified Feynman rules can be applied. The classical
equations of motion and currents are found to be also valid on the quantized
level, and the BRS current for NCQED is derived. We then turn to the more
complicated case of time-space noncommutativity and consider the approach of
TOPT. Additional terms depending on $\theta^{0i}$, which are not present on the
classical level, appear in the quantized equations of motion. We conclude that
the same terms arise in quantized currents and cause the violation of Ward
identities in NCQED. The question of remaining Lorentz symmetry is also
discussed and found to be violated in a simple scattering process. Another
approach to time-space noncommutative theories uses retarded functions. We
present this formalism and discuss the question of unitarity, as well as
equations of motion, and currents. The problems that emerge for
$\theta^{0i}\neq 0$ are seen to arise from a certain type of diagrams. We
propose a modified theory which is unitary and preserves the classical
equations of motion and currents on the quantized level.
