New glass compositions have been investigated in the barium-, indium- and gallium-based glass system (BIG). Radioactive thorium has been completely removed and replaced by gadolinium, and these new glasses have been stabilized by substituting barium by alkali ions. Characteristic temperatures T-g, T-x and T-l, and the Hruby factor, H-r, have been determined for each glass. The most significant critical cooling rates, R(c), are also given : both the highest H-r and the lowest R(c) values for BIG thorium-free glasses were obtained by coupling two alkali ions. Some attempts have also been made to replace thorium by cerium (IV), leading to cerium(III)-containing glasses. The synthesis of cerium(tv)-containing fluoride glasses seemed to be impossible. Nevertheless, CeF4 has been synthesized, the knowledge of its lattice parameters being improved.