We present results of a long-term program for timing the eclipses of eccentric eclipsing binaries. About 40 new precise mid-eclipse times were measured for the eclipsing binary V974 Cyg, RU Mon and V456 Oph. Based on current O-C diagrams, we found in all cases that times of minima besides the typical apsidal motion show additional cyclical changes caused very probably by the third bodies orbiting the eclipsing pair. The periods of apsidal motion are 1470 yr, 361 yr and 22.6 yr, respectively. The period of V456 Oph this is one of the shortest known apsidal-motion periods. The relativistic contributions to the total apsidal-motion rate are significant for V974 Cyg (about 30%) and negligible for RU Mon and V456 Oph (1-2.5%). The third-body orbital periods are relatively short: 30.6 yr, 59.8 yr and 7.4 yr, and their minimal masses are 0.40 M☉, 1.6 M☉, and 0.27 M☉, respectively.
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