The results of μ SR study of the behavior of shallow acceptor centers (AC) in diamond, silicon, and germanium are presented. It was found that the muonic atom, which imitates acceptor in semiconductors, is formed in the paramagnetic state in silicon and germanium at low temperatures whereas in diamond it is formed in the diamagnetic state. The hyperfine interaction constant for the aluminium AC in silicon was estimated for the first time. It was shown that the main contribution to the relaxation of the magnetic moment of the AC is due to interaction of the AC with the phonon via the Roman process in non-degenerated silicon at temperatures ≤ 50 K. In the case of germanium, there is an experimental evidence for a change in the contribution of different phonon processes to the relaxation of the AC at temperature ~10 K. The hole capture rate by the ionized boron acceptor in diamond was determined.