We present new spectroscopic observations of the LINER (and now Seyfer
t 1) nucleus of NGC 1097, and discuss the evolution of its broad, doub
le-peaked Balmer lines. When originally discovered in 1991, the red pe
ak of the double-peaked Ha line was stronger than the blue, while by 1
994 the Ha profile had become almost symmetric and the integrated line
flux had decreased to half its original value. Our new spectrum, take
n in 1996, shows that the broad, double-peaked lines have returned to
almost their original strengths, the profiles of H beta and H alpha ar
e identical to within errors, and the broad-line emitting region is un
reddened. However, the profile of the Balmer lines is now such that th
e blue peak is stronger than the red, opposite to the asymmetry observ
ed in 1991. Various models are considered for the observed behavior, a
ll assuming that the emission lines originate in an accretion disk. We
present a refined version of the precessing, planar, elliptical accre
tion-ring model proposed by Storchi-Bergmann et al. and Eracleous et a
l. This model provides an acceptable fit to the line profiles. We also
consider the possibility that the line-profile evolution results from
a precessing warp in the disk, induced by irradiation from the center
, and show that the range of radii and precession timescales expected
in this model are consistent with the observations. The sudden appeara
nce of the ''disklike'' broad-line profiles in NGC 1097 could have res
ulted from the formation of a new accretion disk due, for example, to
the tidal disruption of a star or the illumination of a preexisting di
sk by a transient ionizing source at the center of the disk.