Wave propagation in the H-guide is investigated theoretically and experimentally. Relationships are derived to describe the field distribution and to calculate the distribution constants of the single- and double-slab guide. Higher modes are studied. The height of the guide can be increased without introducing undamped higher modes. The attenuation coefficients are calculated and analysed for X-band and millimetre wavelengths. Conduction and dielectric losses are considered. Radiation losses and the corresponding attenuation are calculated. The radiation can be arbitrarily reduced by increasing the height of the guide. The maximum transmitted power at electric breakdown is calculated. Experiments are discussed which confirm the theoretically obtained results. The overall results suggest modifications of the original structure and permit the conclusion that the guide is particularly suitable for the frequency range above 20 Gc/s.