  We report detailed follow-up observations of the cataclysmic variable
HS2331+3905, identified as an emission-line object in the Hamburg Quasar
Survey. An orbital period of 81.08min is unambiguously determined from the
detection of eclipses in the light curves of HS2331+3905. A second photometric
period is consistently detected at P~83.38min, ~2.8% longer than the orbital
period, which we tentatively relate to the presence of permanent superhumps.
High time resolution photometry exhibits short-timescale variability on time
scales of 5-6min which we interpret as non-radial white dwarf pulsations, as
well as a coherent signal at 1.12min, which is likely to be the white dwarf
spin period. A large-amplitude quasi-sinusoidal radial velocity modulation of
the Balmer and Helium lines with a period ~3.5h is persistently detected
throughout three seasons of time-resolved spectroscopy. However, this
spectroscopic period, which is in no way related to the orbital period, is not
strictly coherent but drifts in period and/or phase on time scales of a few
days. Modeling the far-ultraviolet to infrared spectral energy distribution of
HS2331+3905, we determine a white dwarf temperature of Teff=10500K (assuming
Mwd=0.6Msun), close to the ZZ Ceti instability strip of single white dwarfs.
The spectral model implies a distance of d=90+-15pc, and a low value for the
distance is supported by the large proper motion of the system, mu=0.14"/yr.
The non-detection of molecular bands and the low J, H, and K fluxes of
HS2331+3905 make this object a very likely candidate for a brown-dwarf donor.
