A description of the frequency characteristics of waveguides with periodic structure is obtained in a general manner from a discussion of loaded transmission lines. An equivalent circuit is analysed to obtain more detailed confirmation of the frequency characteristics. These methods are applied to periodic waveguides with systematic detuning of resonators. All the general features of these types of guide are obtained by elementary reasoning, but for specific design problems a detailed treatment based on Maxwell's field equations is required. This method is used and discussed in the design of a periodic waveguide with every third resonator detuned, for which a space harmonic exists with constant phase-velocity over a wide frequency-band. Experimental methods of checking the theoretical frequency characteristics are discussed, and the results obtained for the constant-phase-velocity guide are given.