Effect of Ga addition on the structure of vitreous As2Se3 is studied using high-resolution X-ray photoelectron spectroscopy and extended X-ray absorption fine structure techniques. The "8-N" rule is shown to be violated for Ga atoms and, possibly, for certain number of As atoms. On the contrary, Se keeps its 2-fold coordination according to "8-N" rule in the amorphous phase throughout all the compositions. Crystalline inclusions appear in the amorphous structure of the investigated glasses at Ga concentrations greater than 3 at. %. These inclusions are presumably associated with Ga2Se3 crystallites and transition phases/defects formed at the boundaries of these crystallites and host amorphous matrix. The existence of Ga-As and Se-Se bonds in the samples with higher Ga content is supported by present studies.