We present some consequences of non-anomalous propagation requirements on various massless fields. Among the models of nonlinear electrodynamics we show that only the Maxwell and Born-Infeld models also obey duality invariance. Separately we show that, for actions depending only on the F-mu nu(2) invariant, the permitted models have L similar to root 1 + F-2. We also characterize acceptable vector-scalar systems. Finally, we find that wide classes of gravity models share with the Einstein model the null nature of their characteristics surfaces.