Hole conductivity and photoluminescence were studied in Mg-doped InN films grown by molecular beam epitaxy. Because surface electron accumulation interferes with carrier type determination by electrical measurements, the nature of the majority carriers in the bulk of the films was determined using thermopower measurements. Mg concentrations in a "window" from ca. 3 × 10 17 to 1 × 10 19 cm −3 produce hole-conducting, p-type films as evidenced by a positive Seebeck coefficient. This conclusion is supported by electrolyte-based capacitance voltage measurements and by changes in the overall mobility observed by Hall effect, both of which are consistent with a change from surface accumulation on an n-type film to surface inversion on a p-type film. The observed Seebeck coefficients are understood in terms of a parallel conduction model with contributions from surface and bulk regions. In partially compensated films with Mg concentrations below the window region, two peaks are observed in photoluminescence at 672 meV and at 603 meV. They are attributed to band-to-band and band-to-acceptor transitions, respectively, and an acceptor binding energy of ∼70 meV is deduced. In hole-conducting films with Mg concentrations in the window region, no photoluminescence is observed; this is attributed to electron trapping by deep states which are empty for Fermi levels close to the valence band edge. * Corresponding author: JWAger@lbl.gov