The theory of the deflecting or hybrid electromagnetic mode in an iris‐loaded waveguide is presented. The dispersion diagrams of the two lowest passbands are computed and compared with experimental data. TM1and TE1modes are no longer independent solutions of Maxwell's equations if the phase velocity equals the velocity of light. In this case the most general field expressions require the use of hybrid solutions, which are derived from Hertzian vectors with transverse components. The hybrid solutions, in contrast to transverse solutions, are able to give a transverse deflection to synchronous, ultrarelativistic particles. The fields in the slot region and the center region of the iris‐loaded waveguide are represented as Fourier series. Matching the four tangential field components results ultimately in an infinite matrix. A vanishing determinant constitutes the relationship between wave number, phase velocity, and geometry. A simple first‐order approximation is derived and interpreted.