This proposed experiment is a muon spin rotation measurement of the hyperfine transition rate in muonic atoms involving a proton or deuteron. The residual spin polarization of a negative muon in gaseous hydrogen will be also measured. The hyperfine transitions are of importance for muon-catalyzed-fusion and muonic atom spectroscopy. On the hyperfine transition rate in muonic protium, only theoretical predictions are known and no measurement had been performed. For a case of muonic deuterium, there is approximately 40% of discrepancy between the experimental result and theoretical calculation. In the proposed experiment, muon spin precession in a static transverse magnetic field will be observed. The precession frequency depends on the hyperfine states of a muonic atom. The goal of the experiment is a systematic determination of the hyperfine rate with the relative uncertainty of 1%.