  Using the bicomplex approach we discuss a noncommutative system in
two--dimensional Euclidean space. It is described by an equation of motion
which reduces to the ordinary sine--Gordon equation when the noncommutation
parameter is removed, plus a constraint equation which is nontrivial only in
the noncommutative case. We show that the system has an infinite number of
conserved currents and we give the general recursive relation for constructing
them. For the particular cases of lower spin nontrivial currents we work out
the explicit expressions and perform a direct check of their conservation.
These currents reduce to the usual sine-Gordon currents in the commutative
limit. We find classical ``localized'' solutions to first order in the
noncommutativity parameter and describe the Backlund transformations for our
system. Finally, we comment on the relation of our noncommutative system to the
commutative sine-Gordon system.
