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We explore the possibility that some of the asymmetric, double-peaked emission lines observed in the spectra of radio-loud AGNs originate in an elliptical accretion disk around a supermassive black hole. This theoretical investigation is motivated by the fact that five of the eighteen double-peaked H$\alpha$ lines found in the spectra of radio-loud AGNs by Eracleous \& Halpern are asymmetric in the opposite sense from what circular, relativistic disk models would predict. We demonstrate that elliptical accretion disks can form in AGNs from the debris released by the disruption of a star by a supermassive black hole, and that such disks can survive for long periods of time without circularizing. We compute emission line profiles expected from an elliptical disk, and compare them with observed double-peaked H$\alpha$ profiles. The precession of the major axis of the elliptical disk can cause the relative sizes of the two peaks to change with time. Another possible cause for variability is the elliptical distortion of a pre-existing circular disk due to a stellar flyby. Such scenarios may be applicable to the well known variability of the double-peaked Balmer lines of the radio galaxy 3C~390.3. We also investigate the applicability of the stellar disruption scenario to the abrupt appearance of asymmetric, double-peaked Balmer lines in the otherwise {\it LINER}-like spectrum of NGC~1097.
