Glass and anti-glass samples of bismuth tellurite (xBi₂O₃–(100 − x)TeO₂) and bismuth niobium tellurite (xBi₂O₃–xNb₂O₅–(100 − 2x)TeO₂) systems were prepared by melt-quenching. The bismuth tellurite system forms glasses at low Bi₂O₃ concentration of 3 to 7 mol%. At 20 mol% Bi₂O₃, the glass forming ability of the Bi₂O₃–TeO₂ system decreases drastically and the anti-glass phase of monoclinic Bi₂Te₄O₁₁ is produced. Structures of glass and the anti-glass Bi₂Te₄O₁₁ samples were studied by high-energy X-ray diffraction, reverse Monte Carlo simulations and Rietveld Fullprof refinement. All glasses have short short-range disorder due to the existence of at least three types of Te–O bonds of lengths: 1.90, 2.25 and 2.59 Å, besides a variety of Bi–O and Nb–O bond-lengths. The medium-range order in glasses is also disturbed due to the distribution of Te–Te pair distances. The average Te–O co-ordination (N_Te–O) in the glass network decreases with an increase in Bi₂O₃ and Nb₂O₅ mol% and is in the range: 4.17 to 3.56. The anti-glass Bi₂Te₄O₁₁ has a long-range order of cations but it has vibrational disorder and it exhibits sharp X-ray reflections but broad vibrational bands similar to that in glasses. Anti-glass Bi₂Te₄O₁₁ has an N_Te–O of 2.96 and is significantly lower than in glass samples.