  We present high- and medium-resolution spectroscopic observations of the
cataclysmic variable BF Eri during its low and bright states. The orbital
period of this system was found to be 0.270881(3) days. The secondary star is
clearly visible in the spectra through absorption lines of the neutral metals
MgI, FeI and CaI. Its spectral type was found to be K3+-0.5. A radial velocity
study of the secondary yielded a semi-amplitude of K_2=182.5+-0.9 km/s. The
radial velocity semiamplitude of the white dwarf was found to be K_1=74+-3 km/s
from the motion of the wings of the Halpha and Hbeta emission lines. From these
parameters we have obtained that the secondary in BF Eri is an evolved star
with a mass of 0.50-0.59 Msun, whose size is about 30 per cent larger than a
zero-age main-sequence single-star of the same mass. We also show that BF Eri
contains a massive white dwarf (M1>1.23 Msun), allowing us to consider the
system as a SN Ia progenitor. BF Eri also shows a high gamma-velocity
(gamma=-94 km/s) and substantial proper motion. With our estimation of the
distance to the system (d~700+-200 pc), this corresponds to a space velocity of
~350 km/s with respect to the dynamical local standard of rest. The cumulative
effect of repeated nova eruptions with asymmetric envelope ejection might
explain the high space velocity of the system. We analyze the outburst
behaviour of BF Eri and question the current classification of the system as a
dwarf nova. We propose that BF Eri might be an old nova exhibiting "stunted"
outbursts.
