  New CCD observations for thirteen eccentric eclipsing binaries from the Large
Magellanic Cloud were carried out using the Danish 1.54-meter telescope located
at the La Silla Observatory in Chile. These systems were observed for their
times of minima and 56 new minima were obtained. These are needed for accurate
determination of the apsidal motion. Besides that, in total 436 times of minima
were derived from the photometric databases OGLE and MACHO. The (O-C) diagrams
of minima timings for these B-type binaries were analysed and the parameters of
the apsidal motion were computed. The light curves of these systems were fitted
using the program PHOEBE, giving the light curve parameters. We derived for the
first time the relatively short periods of the apsidal motion ranging from 21
to 107 years. The system OGLE-LMC-ECL-07902 was also analysed using the spectra
and radial velocities, resulting in masses 6.8, and 4.4 M0 for the eclipsing
components. For one system (OGLE-LMC-ECL-20112), the third-body hypothesis was
also used for describing the residuals after subtraction of the apsidal motion,
resulting in period of about 22 years. For several systems an additional third
light was also detected, which makes these systems suspicious of triplicity.
Based on data collected with the Danish 1.54-m telescope at the ESO La Silla
Observatory.
