We present a calculation of the profiles of emission lines originating
in a relativistic, eccentric disk, and show examples of the resulting
model profiles. Our calculations are motivated by the fact that in ab
out one-quarter of the double-peaked emission lines observed in radio-
loud active galactic nuclei (and in the mildly active nucleus of NGC 1
097), the red peak is stronger than the blue peak, which is contrary t
o the prediction of relativistic, circular disk models. Using the ecce
ntric disk model we fit some of the observed profiles that cannot be f
itted with a circular disk model. We propose two possible scenarios fo
r the formation of an eccentric disk in an active galactic nucleus: (a
) tidal perturbation of the disk around a supermassive black hole by a
smaller binary companion, and (b) formation of an elliptical disk fro
m the debris resulting from the tidal disruption of a star by the cent
ral black hole. In the former case we show that the eccentricity can b
e long-lived because of the presence of the binary companion. In the l
atter case, although the inner parts of the disk may circularize quick
ly, we estimate that the outer parts will maintain their eccentricity
for times much longer than the local viscous time. If any of the obser
ved double-peaked emission lines do indeed arise in an eccentric disk,
their profiles are likely to vary due to precession of the disk, thus
providing a means of testing our proposed scenario. We estimate that
for a black hole with a mass of order 10(6) M. the precision period du
e to general relativistic advance of the pericenter can be as short as
a decade. However, for a black hole with a mass of the order of 10(8)
M. the precession period is of the order of a few centuries, be it du
e to general relativistic effects or due to the tidal effects of a bin
ary companion. We suggest that it may nevertheless be possible to dete
ct profile variability on much shorter timescales by comparing the evo
lution of the line profile with detailed model predictions. We argue t
hat line-profile variability may also be the most promising discrimina
nt among competing models for the origin of asymmetric, double-peaked
emission lines.