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The RadioAstron space radio telescope offers a possibility for testing the gravitational redshift effect with an accuracy of better than 10^{-5}, thus, improving the result of the Gravity Probe A mission by at least an order of magnitude. However, RadioAstron's communications and frequency transfer system doesn't allow for a direct application of the nonrelativistic Doppler and tropospheric compensation scheme used in the Gravity Probe A experiment. This results in a degradation of the redshift test accuracy to approximately 1%. We discuss two approaches to overcome this difficulty and present preliminary results based on data obtained during special observing sessions scheduled for testing the new techniques.