Multiple-beam interference within wave plates is investigated in terms of the detrimental effects it produces in the data of stellar spectropolarimetry. It is noted that spectral fringe structures occur in the phase delay, the polarizance and, for Pancharatnam designs, the reference axis of the wave plate. The natures of the problems are exposed by considering typical wave plates and experimental procedures used in linear and circular spectropolarimetry. It is demonstrated that the chief bane of accurate measurements is the presence of polarizance fringes, but which can be alleviated by the choice of experimental procedure. For spectral circular polarization studies, problems of cross-talk from any linear polarization present in the source are especially severe. In principle the effects of fringing can be removed in data reductions by calibration measurements of a set of linear polarization standard stars displaying different vibration azimuths and, for circular polarization measurements, knowledge of the linear polarization characteristics of the investigated star must also be known.