Recent muon spin-precession experiments confirmed that muonium, a light hydrogen isotope, forms a shallow donor in InN. Depolarization measurements in zero-magnetic field are in agreement and show more than one positively charged center. Below 350 K, one Mu(+) signal has a depolarization function typical of a static center, while a second relaxes more weakly with the characteristics of slow tunneling motion. In combination, spin precession and zero-field data show conclusively that the shallow Mu(0) ionizes to the Mu(+) ground state. The static signal converts to that for the mobile state in two steps, suggesting two metastable Mu(+) trap sites. Preliminary energies are extracted for the detrapping transitions and thermally activated Mu(+) diffusion. (C) 2003 Elsevier B.V. All rights reserved.