  Using the spectroscopies based upon x-ray absorption, we have studied the
structural and magnetic properties of Zn$_{1-x}$Co$_{x}$O films ($x$ = 0.1 and
0.25) produced by reactive magnetron sputtering. These films show
ferromagnetism with a Curie temperature $T_{\mathrm{C}}$ above room temperature
in bulk magnetization measurements. Our results show that the Co atoms are in a
divalent state and in tetrahedral coordination, thus substituting Zn in the
wurtzite-type structure of ZnO. However, x-ray magnetic circular dichroism at
the Co \textit{L}$_{2,3}$ edges reveals that the Co 3\textit{d} sublattice is
paramagnetic at all temperatures down to 2 K, both at the surface and in the
bulk of the films. The Co 3\textit{d} magnetic moment at room temperature is
considerably smaller than that inferred from bulk magnetisation measurements,
suggesting that the Co 3\textit{d} electrons are not directly at the origin of
the observed ferromagnetism.
