We present a series of measurements of the magnetic hysteresis properties of alloys of CuMn in the concentration range 0.06&percent; at. to 4.7&percent; at. when these are cooled well into the spin glass state i.e. T/Tg<0.3. Previous studies (1) made at higher concentrations have revealed the occurrence of a complete reversal of magnetisation in a narrow range of coercive fields and a shifted hysteresis loop. Quite unexpectedly we find that going to lower Mn concentration increases the cooperative nature of the magnetisation reversal to the point where the hysteresis becomes square and that complete, spontaneous (less than 0.1 second time constant) magnetisation jumps are observed in low magnetic field (typically‐150 gauss) together with a shifted square center. We report on the effect on the hysteresis of a number of variables: the magnetisation, the concentration, the temperature, the metallurgy, the time and the application of a static transverse magnetic field. These observations lead to the existence of a well defined anisotropy field in the spin glass state.