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This paper presents analysis of the effects of nonperiodic perturbations in periodic RF structures. Small departures from periodicity change the phase shift experienced by a wave as it traverses an imperfect cell. Cell imperfections may be introduced intentionally or due to fabrication errors or material properties variations. The cumulative effect produces distortions of the fields. If the errors are large enough, the structure modes become localized. This is the first demonstration of field localization in a periodic RF structure. Mechanisms, theory, and analytical relations describing the field distortion and localization phenomena are discussed. The results are demonstrated in periodic structures being investigated for submillimeter wave extended interaction klystrons. In an ancillary result, we discover a fundamental limitation of the finite element as well as other mesh-based codes when applied to long periodic structures.