  We present an extensive study of 162 early-type binary systems located in the
LMC galaxy that show apsidal motion and have never been studied before. For the
ample systems, we performed light curve and apsidal motion modelling for the
first time. These systems have a median orbital period of 2.2 days and typical
periods of the apsidal motion were derived to be of the order of decades. We
identified two record-breaking systems. The first, OGLE LMC-ECL-22613, shows
the shortest known apsidal motion period among systems with main sequence
components (6.6 years); it contains a third component with an orbital period of
23 years. The second, OGLE LMC-ECL-17226, is an eccentric system with the
shortest known orbital period (0.9879 days) and with quite fast apsidal motion
period (11 years). Among the studied systems, 36 new triple-star candidates
were identified based on the additional period variations. This represents more
than 20% of all studied systems, which is in agreement with the statistics of
multiples in our Galaxy. However, the fraction should only be considered as a
lower limit of these early-type stars in the LMC because of our method of
detection, data coverage, and limited precision of individual times of
eclipses.
