The eclipsing variable stars GSC 44870347 and GSC 4513 2537 are recently discovered binary systems (Otero et al., 2006) with orbital periods 1d.99 and 6d.33 days. We carried out the photometric observations of these eclipsing binaries from 2009-2010 using a CCD-array at the Tien-Shan Observatory in Kazakstan, at the Crimea Station of the Sternberg Astronomical Institute, at the Astrokolkhoz Observatory in New Mexico (AAVSO), while the spectrophotometric observations were obtained at the Starlight Farm Observatory in Barnesville, USA.

The use of eccentric eclipsing binaries to test stellar internal structure models, as well as the equations of motion provided by General Relativity, is reviewed. Close to 80 years have elapsed since the first ideas were produced in this field and many results have been obtained since then. It appears that, in general, a good understanding of stellar structure within the main sequence is available while the same level of knowledge can not be claimed beyond the termination age. The equations of general relativity could not be disproved with observational data though some systems cannot still be fully explained. In the near future, the analysis of evolved systems, very low mass stars, the effects of tidal resonances and the presence of third bodies has to be further explored. In addition, the analysis of large data bases obtained by means of extensive photometric surveys will certainly change the picture from an observational point of view.