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Main aim of this paper is the first light curve and apsidal motion analysisof thirteen eccentric eclipsing binaries and to reveal their basic physicalproperties. All of the systems were studied by method of period analysis oftimes of minima and the light curve analysis. Many new times of minima for allof the systems were derived and collected from the data obtained by theautomatic, robotic or satellite telescopes. This allow us to study the apsidalmotion in these systems in detail for the first time. From the light curveanalysis the first rough estimations of the physical properties of thesesystems were done. The analyzed systems undergo an apsidal motion with thefollowing periods in years: AR CMa (44 +/- 10), OZ Hya (117 +/- 53), V498 Mon(62 +/- 4), V521 Mon (217 +/- 37), V684 Mon (74.5 +/- 20), V730 Mon (39 +/-12), GV Nor (197 +/- 67), NS Nor (516 +/- 230), TZ Pyx (157 +/- 37), V385 Sco(1926 +/- 980), V629 Sco (56 +/- 17), V881 Sco (131 +/- 48), V1082 Sco (186 +/-280). Also 190 new minima times were derived and included. The period and lightcurve analyses were done, however a more detailed spectroscopic analysis isneeded to confirm the physical parameters of the components with higherconclusiveness.

On the apsidal-motion of thirteen eclipsing binaries