Nanoparticles of Cox Fe(3-x) O4 with x ranging from 0.05 to 1.6 were synthesized by a combustion reaction method using iron nitrate, cobalt nitrate, and urea as fuel. X-ray diffraction patterns of all systems showed broad peaks consistent with the cubic inverse spinel structure of cobalt ferrite. The absence of extra reflections in the diffraction patterns of as-prepared materials, with x=0.6, 0.8, and 1.0, demonstrates the phase purity. Magnetization measurements show that the saturation magnetization (Ms), coercivity (Hc), and remanent magnetization (Mr) depend on the molar cobalt concentration and the temperature as well. At 4 K, the reduced remanence, Mr Ms, are equal to 0.66 and 0.63 for x=0.8 and 1.0, respectively, indicating that cubic-type magnetic anisotropy is significant in these nanoparticles. These observations are discussed in terms of a model in which it is assumed that each crystallite consists of a ferromagnetic core surrounded by a magnetically disordered shell.