Successive reduction steps of CeO₂ particles by hydrogen between 300 and 1070 K have been followed by temperature-programmed reduction (TPR) and in situ magnetic measurements on several samples with different BET surface areas. The nature of the phases present in cerias reduced between 670 and 1270 K was determined by X-ray analysis. Finally, reoxidation by oxygen or air was studied at room temperature for all the reduced samples. Magnetic and TPR results show a direct relationship between the degree of reduction and the BET surface area. Indeed, for most of the samples, the degree of reduction at 620–670 K determined by magnetism corresponded to the creation of one layer of Ce³⁺ ions at the surface of the ceria. A similar relationship between the BET surface area and the extent of reduction was established using the area of the low-temperature TPR composite peak, the maximum of which was found to be constant at 810 K. When the reduction progresses further into the bulk, two main phases were evidenced: first, and expanded cubic CeO_{2 –x} phase derived from the initial ceria by a dilatation of the whole structure and, for deeply reduced samples, the hexagonal Ce₂O₃ phase. A new intermediate phase, cubic Ce₂O₃, was also observed on samples reduced at 1070–1170 K. Complete reoxidation by oxygen occurs at room temperature, for all reduction percentages below ca. 60 %, i.e. as long as the reduced phase remained in the cubic form. When the hexagonal Ce₂O₃ phase has been formed, the reoxidation cannot be completed at 294 K.