This proposal is part of a long-range program aiming at determining the stable charge-state configurations, site and impurity energy levels (donor and/or acceptor) of hydrogen in widegap oxides with important technological applications, by means of the analogy with muonium. In this proposal we concentrate on zirconium oxide (ZrO2) in its cubic form (magnesium stabilized) and address:i) the shallow and the deep muonium state, by means of high-statistics transverse-field and longitudinal-field repolarization measurements, respectively, in order to obtain the hyperfine interaction and the activation energy; ii) the diffusion of Mu^+, by means of transverse field measurements. Additional measurements in yttrium-stabilized ZrO2 are proposed in order to begin the investigation of the diffusion parameters with the stabilizing cation.