The short-range order structures in some ternary ZrF₄-BaF₂-based glasses doped with EuF₃, AlF₃ or NaF are studied by XAFS. The near-neighbour structures around Zr, Ba and Eu are determined and compared with that in binary ZrF₄-BaF₂ glasses. The structural parameters of near neighbours around Zr and Ba are slightly reduced on addition of NaF or AlF₃. Also, it is observed that the intensities of the 'white lines' in the L_n and L_m absorption edges of Eu and Ba in these glasses are different from those in corresponding fluorides. The causes leading to these changes are discussed. Meanwhile the differences between the bonding behaviour of Eu-F and that of Ba-F in the glasses are also discussed.