It is suggested that the orthodox theory of multimode cavities, that there are two modes, a TE and a TM, to each eigenvalue root of the well-known resonance equation, is incomplete, and that there are three modes corresponding to three mutually orthogonal directions ofpropagation within the cavity for each mode-number.The analysis is based on considering a rectangular cavity as three waveguides in three propagation directions, in each case terminated in short-circuit plates at their ends.It is found that in general the characteristic wave impedances of the two sets of three modes are all different, giving six values for each mode-number. Although all six modes with the same mode-number have the same resonant frequency, they must be considered as separate modes because of their different characteristic impedances.The thesis provides an insight into multimode cavity operation, and explains, inter alia, a prime mechanism of edge-heating effects frequently observed, the unusual versatility of a multimode oven...