Muonium centers (Mu) in single crystals and powdered alkali halides have been studied using the high-timing-resolution transverse field μSR technique. Mu has been observed and its hyperfine parameter (HF) determined in every alkali halide. For the rocksalt alkali halides, the HF parameter Aμ shows a systematic dependence on the host lattice constant. A comparison of the Mu HF parameter with hydrogen ESR data suggests that the Mu center is the muonic analogue of the interstitial hydrogen Hi0-center. The rate of Mu diffusion can be deduced from the motional narrowing of the nuclear hyperfine interaction. KBr shows two different Mu states, a low-temperature MuI-state and a high-temperature MuII-state. © 1986 J.C. Baltzer A.G., Scientific Publishing Company.