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We present a comparative study of the high-pressure behaviours of the nuclear waste immobilisation materials zirconolite-2M,− 4M,–3O, and− 3T. The materials are studied under high-pressure conditions using synchrotron powder X-ray diffraction. For zirconolite-2M we also performed density-functional theory calculations. A new triclinic crystal structure (space group P 1¯), instead of the previously assigned monoclinic structure (space group C2/c) is proposed for zirconolite-2M. We named the triclinic structure as zirconolite-2TR. We also found that zirconolite-2TR undergoes a phase transition at 14.7 GPa to a monoclinic structure described by space group C2/c, which is different than the high-pressure structure previously proposed in the literature. These results are discussed in comparison with previous studies on zirconolite-2M and the related compound calzirtite. For the other three zirconolite structures (4M …