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We present some consequences of non-anomalous propagation requirements onvarious massless fields. Among the models of nonlinear electrodynamics we showthat only Maxwell and Born-Infeld also obey duality invariance. Separately weshow that, for actions depending only on the $F_\mn^2$ invariant, the permittedmodels have $L \sim \sqrt{1 + F^2}$. We also characterize acceptablevector-scalar systems. Finally we find that wide classes of gravity modelsshare with Einstein the null nature of their characteristic surfaces.Comment: 11 pages, LaTeX, no figure

`Good propagation' and duality invariance constraints on scalar, gauge vector and gravity actions