Abstract
The paper describes a target setting of searching for apsidal motion in 21 eclipsing binaries. We estimate the capability of its determination for the systems of interest in the coming years, as well as present results of observations in 2009–2018, in which the minima of the light curves of these stars have been obtained. The accuracy of orbital period determination of the studied binaries is 10–100 times greater in comparison with the previously available data. For two systems, photometric elements are determined. As a by-product of the study, a close eclipsing binary of the W UMa type was discovered.