Exciton luminescence of non-doped and newly prepared gallium-doped ZnO epitaxial thin films deposited onto sapphire substrates in a low-pressure system within a single chemical vapor deposition cycle is studied depending on films thickness as well as the doping degree. It is shown that the thickness dependence of the ratio between the integral intensities of single-phonon and double-phonon lines allows one to estimate the transition layer thickness.