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We investigated Zn0.94 Co0.06 O thin films on sapphire (0001) substrates with respect to their structural and magnetic properties. X-ray diffraction shows a c axis oriented growth and no secondary phases within its resolution. A clear improvement of the crystalline quality was obtained by post annealing under vacuum conditions. Further information about the local electronic structure is obtained by X-ray absorption spectroscopy at the Co L 2,3 and the O K edge. Magnetic properties were investigated with a superconducting quantum interference device (SQUID) and by X-ray magnetic circular dichroism at the Co L 2,3 edge. Both techniques yield mainly paramagnetic behavior of the samples. For low temperatures, an additional small ferromagnetic contribution was observed in SQUID measurements. Several possible origins of this ferromagnetic contribution are discussed.