  We study the noncommutative generalization of (euclidean) integrable models
in two-dimensions, specifically the sine- and sinh-Gordon and the U(N)
principal chiral models. By looking at tree-level amplitudes for the
sinh-Gordon model we show that its na\"\i ve noncommutative generalization is
{\em not} integrable. On the other hand, the addition of extra constraints,
obtained through the generalization of the zero-curvature method, renders the
model integrable. We construct explicit non-local non-trivial conserved charges
for the U(N) principal chiral model using the Brezin-Itzykson-Zinn-Justin-Zuber
method.
