Low-temperature crystal structure of the Er_xDy_1−xAl₂ alloys with x = 0.45, 0.67, 0.90 was examined using temperature-dependent powder X-ray diffraction. The Er-rich sample, Er_0.9Dy_0.1Al₂, exhibits a rhombohedral distortion associated with the magnetic ordering that occurs around 20 K. The rhombohedral distortion is suppressed in Er_0.67Dy_0.33Al₂, while a weak low-temperature tetragonal distortion is observed in Er_0.45Dy_0.55Al₂. The mean-field theory supports the correlation between the type of structural distortion and the variable easy magnetization axis in Er_xDy_1−xAl₂ intermetallics.