  This is the second part of a work aimed to study complex-phase oscillatory
solutions of nonlinear symmetric hyperbolic systems. We consider, in
particular, the case of one space dimension. That is a remarkable case, since
one can always satisfy the \emph{naive} coherence condition on the complex
phases, which is required in the construction of the approximate solution.
Formally the theory applies also in several space dimensions, but the
\emph{naive} coherence condition appears to be too restrictive; the
identification of the optimal coherence condition is still an open problem.
