Scanning near-field photoluminescence (PL) spectroscopy was applied to study spatial variations of emission spectra of AlxGa1-xN epilayers with 0.6 <= x <= 0.7. PL spectra were found to be spatially uniform with peak wavelength standard deviations of only similar to 2 meV and ratios between peak intensity standard deviations and average peak intensity values of 0.06. The observed absence of correlation between the PL peak wavelength and intensity shows that spatial distribution of nonradiative recombination centers is not related to band potential fluctuations. Our results demonstrate that the homogeneous broadening and the random cation distribution primarily determine PL line-widths for layers grown under optimized conditions.