  We present the shock-free wave propagation requirements for massless fields.
First, we briefly argue how the "completely exceptional" approach, originally
developed to study the characteristics of hyperbolic systems in 1+1 dimensions,
can be generalized to higher dimensions and used to describe propagation
without emerging shocks, with characteristic flow remaining parallel along the
waves. We then study the resulting requirements for scalar, vector,
vector-scalar and gravity models and characterize physically acceptable actions
in each case.
