Muon-spin-rotation measurements in the group I-VII semiconductors CuCl, CuBr, and CuI reveal muonium centers with weak isotropic hyperfine (hf) parameters which range between 0.2716 and 0.3744 times the hf parameter for muonium in vacuum. The observed centers display several unusual characteristics when compared with muonium in other tetrahedrally coordinated materials. In particular the hf parameters in the copper halides are much smaller than expected on the basis of their ionicity. Also, in CuCl and CuBr two distinct muonium centers (MuI and MuII) with almost identical isotropic hf parameters are observed for the first time. The MuI center is populated preferentially at low temperature but makes a thermally activated transition to MuII, indicating that MuI is less stable than MuII. Measurements of the line broadening in the magnetic field region 0.21.2 T indicate that there is no motional averaging of the nuclear hyperfine interaction and therefore that the centers are close to being static. © 1986 The American Physical Society.