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Attention is called to the existence of microwave resonances which have the unusual property that they are nonradiating, and thus have high Q, in spite of the fact that the fields are not enclosed completely by metallic walls. These "ghost modes" represent fields which are derived from those of the usual waveguide modes, but are "trapped" in the vicinity of imperfections in the waveguide. Their resonant frequency is slightly lower than the corresponding cutoff frequency. If one attempts to use a waveguide in its lowest mode, over a range of frequencies which includes the ghosts of higher modes, complicated resonance effects may be observed which can cause trouble in some types of microwave circuits. The same phenomenon exists in any structure which has pass bands and rejection bands, such as periodic structures or crystals.