Spectral, temporal, and polarisation characteristics of luminescence of heavily doped AlxGa1-xN films on a sapphire substrate are studied under pulsed pumping at the wavelength λ = 266 m. Spectra of spontaneous emission related to donor-acceptor transitions are inhomogeneously broadened with the FWHM of above 0.5 eV and cover the entire visible range. Spectra of radiation emitted from an edge of investigated structure comprise several narrow-band equidistant components, each of them being split to TE and TM modes with mutually orthogonal polarisations. This is related to plane waves propagating inside a plane waveguide along a zigzag path in the conditions of total internal reflection from waveguide surfaces. The optical gains measured for Al0.5Ga0.5N/AlN at λ ≈ 510 nm, Al0.74Ga0.26N/AlN at λ ≈ 468 nm, and AlN/Al0.6Ga0.4N/AlN/Al2O3 at λ ≈ 480 nm were, respectively, ∼70, 20, and 44 cm-1. The luminescence quantum efficiencies measured for Al0.74Ga0.26N, Al0.65Ga0.35N, and Al0.5Ga0.5N films are, respectively, 0.79, 0.49, and 0.14; the transition cross sections calculated at emission band centres are ∼10-18 cm2.