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A new series of 20-component fluorite-based compositionally complex oxides (20CCFBOxNb/Ta) with the general chemical formula (15RE1/15)2x+1(Ce1/3Zr1/3Hf1/3)3-3x(Nb1/2Ta1/2)xO8-delta (0 <= x <= 1, where 15RE1/15 = La1/15Pr1/15Nd1/15Sm1/15Eu1/15Gd1/15Tb1/15Dy1/15Y1/15Ho1/15Er1/15Tm1/15Yb1/15Lu1/15Sc1/15) are synthesized. Despite that the Gibbs phase rule allows for the existence of up to 20 phases at the thermodynamic equilibrium, 17 of the 20CCFBOxNb/Ta compositions synthesized in this study all possess single ultrahigh-entropy phases in fluorite, pyrochlore, or weberite structure, as shown by X-ray diffraction (XRD). Only < 1 vol.% of secondary phases are observed in two compositions near the phase-transition points. With changing compositional variable x, this series of 20CCFBOxNb/Ta undergoes an abrupt fluorite-pyrochlore transition at x = ~0.27 and an abrupt pyrochlore-weberite transition at x = ~0.87. Careful characterization reveals abrupt changes of order parameters at both phase transitions. In addition, weberite short-range ordering can persist into the long-range pyrochlore phase, which leads to the lowest thermal conductivities.