  Spectroscopy and V,I CCD photometry of the dwarf irregular galaxy SBS
1129+576 are presented for the first time. The CCD images reveal a chain of
compact H II regions within the elongated low-surface-brightness (LSB)
component of the galaxy. Star formation takes place mainly in two
high-surface-brightness H II regions. The mean (V-I) colour of the LSB
component in the surface brightness interval between 23 and 26 mag/sq.arcsec is
relatively blue ~0.56+/-0.03 mag, as compared to the (V-I)~0.9-1.0 for the
majority of known dwarf irregular and blue compact dwarf (BCD) galaxies.
Spectroscopy shows that the galaxy is among the most metal-deficient galaxies
with an oxygen abundance 12+log(O/H)= 7.36+/-0.10 in the brightest H II region
and 7.48+/-0.12 in the second brightest H II region, or 1/36 and 1/28 of the
solar value, respectively. Hbeta and Halpha emission lines and Hdelta and
Hgamma absorption lines are detected in a large part of the LSB component. We
use two extinction-insensitive methods based on the equivalent widths of (1)
emission and (2) absorption Balmer lines to put constraints on the age of the
stellar populations in the galaxy. In addition, we use two extinction-dependent
methods based on (3) the spectral energy distribution (SED) and (4) the (V-I)
colour. The observed properties of the LSB component can be reproduced by a
stellar population forming continuously since 10 Gyr ago, provided that the
star formation rate has increased during the last 100 Myr by a factor of 6 to
50 and no extinction is present. However, the observational properties of the
LSB component can be reproduced equally well by continuous star formation which
started not earlier than 100 Myr ago and stopped at 5 Myr, if some extinction
is assumed.(Abridged)
