Using X-Ray Diffraction, Scanning Electron Microscopy, and Superconducting Quantum Interference Device magnetometer, detailed structural, morphological, and magnetic properties are reported on undoped and cobalt doped ZnO Dilute Magnetic Semiconductors, which were prepared by the hydrothermal method. Synthesis of undoped ZnO and cobalt-doped ZnO nanorods was carried out using aqueous solutions of Zn(NO3)(2) center dot 6H(2)O, Co(C2H3OO)(2) center dot 4H(2)O, and NH4OH as hydrolytic catalyst. Samples of different sizes and shapes were synthesized by varying process parameters such as solution molarity (0.05M, 0.15M, 0.3M, 0.5M), pH of the precursors in the range 8-11, growth temperature (100 degrees-130 degrees C), growth time (3-6 hrs), and annealing time. Optimum synthesis parameters to grow ZnO and cobalt-doped ZnO nanorods have been obtained. These nanorods show paramagnetic-like behavior. Our results do not indicate ferromagnetism behavior, unlike reported in thin films and nanocrystalline samples. The differences are likely due to the possible role of nanoparticle size, shape, and different oxygen vacancy concentrations.