  LINER nuclei, which are present in many nearby galactic bulges, may be the
manifestation of low-rate or low-radiative-efficiency accretion onto
supermassive central black holes. However, it has been unclear whether the
compact UV nuclear sources present in many LINERs are clusters of massive
stars, rather than being directly related to the accretion process. We have
used HST to monitor the UV variability of a sample of 17 galaxies with LINER
nuclei and compact nuclear UV sources. Fifteen of the 17 galaxies were observed
more than once, with two to five epochs per galaxy, spanning up to a year. We
detect significant variability in most of the sample, with peak-to-peak
amplitudes from a few percent to 50%. In most cases, correlated variations are
seen in two independent bands (F250W and F330W). Comparison to previous UV
measurements indicates, for many objects, long-term variations by factors of a
few over decade timescales. Variability is detected in LINERs with and without
detected compact radio cores, in LINERs that have broad H-alpha wings detected
in their optical spectra (``LINER 1's''), and in those that do not (``LINER
2s''). This variability demonstrates the existence of a non-stellar component
in the UV continuum of all types, and sets a lower limit to the luminosity of
this component. We note a trend in the UV color (F250W/F330W) with spectral
type - LINER 1s tend to be bluer than LINER 2s. This trend may indicate a link
between the shape of the nonstellar continuum and the presence or the
visibility of a broad-line region. In one target, the post-starburst galaxy NGC
4736, we detect variability in a previously noted UV source that is offset by
2.5" (60 pc in projection) from the nucleus. This may be the nearest example of
a binary active nucleus, and of the process leading to black hole merging.
