We present the results of an electron paramagnetic resonance study of homogeneous single phase Zn1-xMnxO thin films with Mn concentrations varying between x=0.07 and x=0.34. Our results show antiferromagnetic (AF) coupling in the entire concentration range with an effective exchange integral of J/kB=-21.8 K for x≤0.16 much stronger than in the CdMn(S,Se,Te) series. We observe deviations from the Curie-Weiss behavior for concentrations above x=0.16 and show this to be a “universal” behavior of II-VI diluted magnetic semiconductors. Our results demonstrate that AF interactions are dominating in n-type Zn1-xMnxO (x≫0.07) with a carrier concentration of 1018 cm-3 contrary to previous claims. These AF interactions are responsible for high spin freezing temperatures and absence of magnetic long range order.