  We report the very first analysis of 27 eclipsing binary systems with high
eccentricities that sometimes reach up to 0.8. The orbital periods for these
systems range from 1.4 to 37 days, and the median of the sample is 10.3 days.
Star CzeV3392 (= UCAC4 623 022784), for example, currently is the eclipsing
system with the highest eccentricity (e = 0.22) of stars with a period shorter
than 1.5 days. We analysed the light curves of all 27 systems and obtained the
physical parameters of both components, such as relative radii, inclinations,
or relative luminosities. The most important parameters appear to be the
derived periods and eccentricities. They allow constructing the
period-eccentricity diagram. This eccentricity distribution is used to study
the tidal circularisation theories. Many systems have detected third-light
contributions, which means that the Kozai-Lidov cycles might also be
responsible for the high eccentricities in some of the binaries.
