Two disordered alloys, Au81Fe19 and Ni79Mn 21, were cooled from ∼ 100 K down to different temperatures in the range 1.2 K < T < 40 K, either in zero field or in a field ranging from 50 G to 28 kG. Their low-field hysteresis loops were then measured Near and above some characteristic temperature, TAT, identified as the de Almeida-Thouless temperature, the hysteresis loops of both alloys present essentially the same shape as for standard ferromagnets. Well below TAT, the loops become quite large and are very different in shape both from the standard ferromagnetic case and from one alloy to another. Memory effects, induced by field cooling, are found to have very different stabilities in the two alloys. In Au 81Fe19, they are highly unstable and easily washed out by cycling an applied field of a few hundreds gauss at 1.5 K. In the Ni 79Mn21 alloy, they are remarkably stable whatever the cycling field (T = 1.5 K) in the available range ± 28 kG. Large hysteresis losses set in below TAT and increase very rapidly in a narrow temperature region defined as the de Almeida-Thouless cross-over region. It is suggested that the low field behaviour of Ni79Mn21 cooled in zero field is determined by the appearance of unidirectional anisotropy fields during cooling. These fields would have approximately the same domain structure as the spontaneous magnetization and would be created by the molecular field of this magnetization.