This paper reports on the magnetic properties of Zn1-xMnxO with Mn concentrations from 5% to 25%. The polycrystalline films, deposited by pulsed laser deposition on c-oriented sapphire and mica substrates, were first characterized by x-ray diffraction, absorption, and fluorescence, as well as by photoelectron and optical spectroscopy. Except for the highest Mn content films, all films are single-phase wurtzite, with Mn in tetrahedral coordination. Films with 25% Mn show traces of other crystal phases with spinel or perovskite structure. Their magnetization was then measured in function of applied magnetic field in the range -5 to 5 T and temperature in the range 1.8 to 300 K. All single-phase films exhibit paramagmetic behavior in the whole temperature range. Ferri- or ferromagnetic behavior (involving only a small proportion of the total magnetization) is found only in samples with other phases or in the sapphire substrates. The paramagnetic susceptibility increases with the Mn content. However, the decrease in the mean magnetic moment per Mn atom with increasing Mn concentration and the temperature dependence of the magnetic susceptibility around 1.8 K provide strong evidence of antiferromagnetic interaction between second neighbor Mn atoms.