Nanomaterials based on zinc oxide co-doped with copper and aluminum of varying concentrations were obtained using the sol-gel technology adapted to solve problems of nanostructural engineering. Experimental scanning electron  microscopy data show that varying the concentration of co-dopants allows flexible control of the nanomaterial structure. Optical properties of ZnO:Al:Cu were studied in the visible and ultraviolet radiation ranges. It was found for all  the studied samples that there is an insignificant decrease in radiation transmission compared to unmodified zinc oxide, while they still remain optically transparent. A non-monotonic dependence of the band gap of the nanomaterials  on the concentration of co-dopants was established. Our findings suggest that the variability of the optical band gap in the ZnO sample containing 4 at.% Al and 2 at.% Cu is a consequence of the manifestation of size quantization  effects.