In this work, we present a study of the behavior of linewidths of excitonic photoluminescence transitions measured at 10 K in AlGaN alloys as a function of Al concentration. Samples we have investigated are grown by low-pressure metalorganic chemical vapor deposition on (0001) oriented sapphire substrates with low-temperature GaN buffer layers. The Al composition ranged from 0%-35%. We find that the values of the excitonic linewidth increase as a function of Al concentration and agree very well with those calculated using a model in which the broadening effect is assumed to be due to compositional disorder in semiconductor alloys. The values of the excitonic linewidths measured in our samples are considerably smaller than those reported recently, thus attesting to the high quality of our samples.