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N. V. Nunes, D. A. Litvinov, V. N. Rudenko, M. V. Zakhvatkin, N. Bartel at al The incompatibility of general relativity and quantum theory is a fundamental problem in our understanding of the physical world. The Einstein equivalence principle (EEP) is at the foundation of general relativity and the gravitational redshift is a consequence of the EEP. An accurate measurement of the gravitational redshift and a comparison with prediction is therefore of prime importance. The space VLBI satellite RadioAstron was launched in 2011 into a highly elliptical orbit around Earth with an apogee of ~350,000 km. For several years, the downlink signals at 8.4 and 15 GHz were locked to the on-board hydrogen maser, and their frequencies were recorded at ground stations also equipped with hydrogen masers. Over 4,250 sessions, most with ∼100,000 frequency recordings at each of the two frequencies, were obtained over ~4.5 years. During the 9-day elliptical orbits, the spacecraft traveled through the varying gravitational potential of Earth, which caused an oscillating gravitational redshift of the downlink signals. The relative frequency shift varied between 6.8×10^−10 and ∼ 4×10^−10. We report on our analysis of data recorded at the ground stations in Pushchino, Russia, and Green Bank, USA, compare our results with predictions, and discuss the possibility of testing the EEP with a higher sensitivity than that of the Gravity Probe A mission.