The propagation behaviour is described of a number of periodically loaded circular waveguide structures containing either dielectric or axially magnetised ferrimagnetic material. The structures include the disc-loaded axial rod and tube. Dispersion characteristics are theoretically determined and the dependence of the lower and upper cutoff frequencies upon various structural and material parameters is studied. For the ferrite structure, two passbands are observed for each mode, one occurring below ferrimagnetic resonance, the other occurring above resonance. The centre frequency of the passband can be varied by changing the strength of the axial applied magnetic field. Experimental dispersion characteristics are shown for both dielectric and ferrite structures, and these are found to agree well with those predicted theoretically.