Investigations on luminescent properties of good‐quality GaN single‐crystalline epitaxial layers at temperatures in the range 1.6–300 K are reported. The high‐energy region (3.27–3.48 eV) at 1.6 K is dominated by different bound exciton transitions. Peaks are observed at 3.469, 3.454, 3.447, 3.400, 3.377, 3.355, and 3.287 eV at 1.6 K in this region; their possible origin is discussed. At higher temperatures (T> 30 K) the freeA‐exciton emission is also clearly observed, and thus its positionEAx=3.475±0.0005 eVat 1.6 K could be established (neglecting polariton effects) together with a value of 6.4±0.4 meV for the binding energy of an exciton to a neutral donor. The energy region 3.0–3.3 eV is dominated by the previously studied donor‐acceptor pair spectra, which peak at 3.263±0.003 in all our good‐quality samples (undoped and doped). From the assignment of a subsidiary high‐energy peak as free‐to‐bound transitions, a value of 29±6 meV for the donor binding energy is experimentally determined, in good agreement with the theoretical effective mass value. The region below 3.0 eV is in Cd‐doped material dominated by a broad band centered at 2.72 eV, unlike previous observations. This band is an envelope composed of several discrete series of emissions observable at low temperatures. The solubility of Cd in GaN appears to be rather low, and high‐Ohmic single‐crystalline material was not obtained, in contrast to our results from Zn‐doping.