Studies of the magnetic properties of crystals of the mixed semiconductors Cd1-xMnxTe indicate that: (i) for x ≤ 0.17 the crystals are paramagnetic at all temperatures, (ii) for 0.17 <x ≤ 0.60 a spin glass phase and (iii) for 0.60 <x ≤ 0.71 an antiferromagnetic ordering are observed at low temperatures. Neutron diffraction experiments have shown that for 0.60 <x <0.70 the particular peaks observed could be interpreted in terms of type III antiferromagnetic ordering of the f.c.c. sublattice. The temperature dependence of the integrated intensities of the magnetic reflections follows the square of the Brillouin function for S = 5/2, except above 3/4 of the ordering temperature. Above this temperature, the observed intensities are larger than expected from ordinary critical fluctuations near a second order phase transition. For x = 0.70, a detailed study has shown that this phenomenon suggests that the spins of the randomly distributed Mn atoms are ordered in clusters. A rather large discrepancy between the ordering temperatures obtained by neutron scattering and by other techniques is explained by a phenomenological description of the transition process.