NOVELTY - Manufacturing a (non)doped powder particles of zirconium and/or hafnium oxide, comprises calcination or hydrothermal treatment of powder of a starting particle in a material comprising: a zirconium and/or hafnium derivative (I), where the material has a solubility of less than 10-3 mol/l in water at a temperature of less than 20 degrees C, the derivative is (non)doped; and/or a zirconium hydrate and/or hafnium hydrate (II).    USE - The process is useful for the preparation of (non)doped powder particles of zirconium and/or hafnium oxide, which is useful in catalysis and filtration.    ADVANTAGE - The process is simple and efficient to obtain the powder with high specific surfaces and/or new forms.    DETAILED DESCRIPTION - Manufacturing a (non)doped powder particles of zirconium and/or hafnium oxide and their mixtures, comprises calcination or hydrothermal treatment of powder of a starting particle in a material comprising: a zirconium and/or hafnium derivative of formula (M(OH)x (N1)y(OH2)z) (I), where the material has a solubility of less than 10-3 mol/l in water at a temperature of less than 20 degrees C, the derivative is (non)doped; and/or a zirconium hydrate and/or hafnium hydrate of formula (MOx(OH)y(OH2)z) (II), where the starting particles are hydrate, the powder has a porosity index of greater than 2, the porosity index is equal to the ratio (Asr)/(Asg), the Asg is theoretical specific surface area of the powder particles and the Asr is measure of the actual specific surface area by Brauner-Emmett-Teller (BET), and the starting particles are obtained from a (non)aggregated base particles, having a sphericity index of less than 0.6. In formula (I):    M = Zr4-, or Hf4-;    N1 = anion or its mixture;    x, y = positive numbers; and    z = a positive number or zero.    In formula (II):    M = Zr4-, and/or Hf4-;    x, z = positive numbers or zero; and    y = positive number, where 2x+y is 4.    INDEPENDENT CLAIMS are included for:    (1) a powder having a maximum particle size of less than 200 mu m and having a porosity index of greater than 2, where the porosity index is equal to the ratio (Asr)/(Asg), the Asg is theoretical specific surface area of the powder particles and the Asr is a measure of the actual specific surface area by BET, where the powder: comprises greater than 20% in number of (non)aggregated base particle; has a sphericity index of greater than 0.6; comprises aggregates in the form of stars containing 3-15 branches or strips constituted of 2-50 plaquettes; and comprises zirconium oxide and/or hafnium oxide of formula ((MO)x) (III); and    (2) a device comprising a catalyst, a catalyst support, a filtration component, a component of a fuel cell, a piezoelectric material, an optical connector, a dental ceramic, structural ceramic, or obtained from the powder.    M = Zr4- and/or Hf4-; and    x = positive numbers or zero.