Double electron-muon resonance (DEMUR) is reported on anomalous muonium centers in silicon. Resonance of EPR transitions otherwise non-observable is detected by characteristic structure in the muon-spin-rotation (SR) spectra. In order to explain the nature of this structure, the theory of DEMUR is extended to include inhomogeneous broadening of the EPR and SR transitions owing to nuclear hyperfine interactions with the Si29 nuclei present. The principal effect of this extension is that only one of the two SR lines is split rather than both as predicted when nuclear hyperfine effects are neglected. © 1986 The American Physical Society.