The application of the concept of intrinsic modes to the theory of propagation in conical corrugated horns is developed. An intrinsic mode is an exact solution of source-free Maxwell equations which satisfies the boundary conditions to a prescribed order of accuracy as the flare angle α becomes small. There exists an infinite number of intrinsic modes for a given structure and each one corresponds with a fixed local normal mode at every cross-section, to which it approximates asymptotically as α → 0. An intrinsic mode is given by a Fourier-like spectral integral which is uniformly valid, including the regions where the corresponding local normal mode is evanescent or in transition from propagating to evanescent. This spectral integral can be generated from knowledge of onlyonelocal normal mode at each cross-section, and numerical calculations show that the intrinsic mode based on theHE11local normal mode is sufficient for many applications, including the calculation of crosspolar radiation.