Heat capacities of hafnium-oxygen alloys, HfOX (X = 0.14, 0.17 and 0.19), were measured from 325 to 905 K by using an adiabatic scanning calorimeter. A lambda type heat capacity anomaly was observed around 700 K for all the samples, and was assigned to an order-disorder rearrangement of oxygen atoms. The measured values for the entropies of the order-disorder transition are in good agreement with the theoretical values in the composition range of X less than or equal to 1/6 (X = 0.14 and 0.17), but smaller than the theoretical value in the range of X > 1/6 (X = 0.19). Another heat capacity anomaly was observed at a temperature lower than that of the order-disorder transition for the well-annealed samples. The appearance of this anomaly depends on the annealing conditions of the samples.