  Aims: As part of our observational projects at the La Silla Danish 1.54-meter
telescope, we aim to measure the precise times of minimum light for eccentric
eclipsing binaries in the Large Magellanic Cloud, needed for accurate
determination of apsidal motion. Many new times of minima were derived from the
photometric databases OGLE and MACHO. Several new minima were also observed.
Five early-type and eccentric-orbit eclipsing binaries: HV 982 (P = 5.34 d, e =
0.15), HV 2274 (5.73 d, 0.17), MACHO 78.6097.13 (3.11 d, 0.05), MACHO
81.8881.47 (3.88 d, 0.22), and MACHO 79.5377.76 (2.64 d, 0.06) were studied.
Methods: The O-C diagrams of the systems were analysed using all reliable
timings found in the literature, and new or improved elements of apsidal motion
were obtained. Light and radial velocity curves of MACHO 81.8881.47 and MACHO
79.5377.76 were analysed using the program PHOEBE. Results: We derived for the
first time or significantly improved the relatively short periods of apsidal
motion of 211 (12), 127 (8), 48 (13), 103 (20), and 42 (19) years,
respectively. The internal structure constants, log k2, were found to be -2.37,
-2.47, -2.17, -2.02, and -1.86 respectively, under the assumption that the
component stars rotate pseudosynchronously. The relativistic effects are weak,
up to 6% of the total apsidal motion rate. The masses for MACHO 81.8881.47
resulted in 5.51 (0.21) and 5.40 (0.19) M0, while for MACHO 79.5377.76 the
masses are 11.26 (0.35) and 11.27 (0.35) M0, respectively.

Solar and Stellar Astrophysics