The review describes experimental and theoretical results on the determination of the frequency ω₀ of the hyperfine splitting of a muonium atom in a medium. The papers from the I. V. Kurchatov Atomic Energy Institute in which the method of the two-frequency precession of muonium for the determination of the frequency ω₀ was first proposed are examined in greater detail. The data obtained add in an essential manner to the available information on the interaction of an impurity hydrogenlike atom in condensed media.