  Aim: Our purpose is to provide reliable stellar parameters for a significant
sample of eclipsing binaries, which are representative of a whole dwarf and
metal-poor galaxy. We also aim at providing a new estimate of the mean distance
to the SMC and of its depth along the line of sight for the observed field of
view. Method: We use radial velocity curves obtained with the ESO FLAMES
facility at the VLT and light curves from the OGLE-II photometric survey. The
radial velocities were obtained by least-squares fits of the observed spectra
to synthetic ones, excluding the hydrogen Balmer lines. Results: Our sample
contains 23 detached, 9 semi-detached and 1 overcontact systems. Most detached
systems have properties consistent with stellar evolution calculations from
single-star models at the standard SMC metallicity Z = 0.004, though they tend
to be slightly overluminous. The few exceptions are probably due to third light
contribution or insufficient signal-to-noise ratio. The mass ratios are
consistent with a flat distribution, both for detached and
semi-detached/contact binaries. A mass-luminosity relation valid from ~4 to ~18
Msol is derived. The uncertainties are in the +-2 to +-11% range for the
masses, in the +-2 to +-5% range for the radii and in the +-1 to +-6% range for
the effective temperatures. The average distance modulus is 19.11+-0.03
(66.4+-0.9 kpc). The moduli derived from the V and from the I data are
consistent within 0.01 mag. The 2-sigma depth of the SMC is, for our field, of
0.25 mag or 7.6 kpc under the assumption of a gaussian distribution of stars
along the line of sight. Three systems show significant apsidal motion, one of
them with an apsidal period of 7.6 years, the shortest known to date for a
detached system with main sequence stars.
