Abstract: Special features in the phase diagram and in the low temperature hysteresis cycles have been experimentally observed in the complex CeNi1-xCux system. We present also here theoretical approaches, based firstly on a Kondo lattice model which describes the coexistence between a spin glass or a cluster glass state, the Kondo regime and the ferromagnetic ordering. The second model is a Monte Carlo simulation on a 3D lattice with clusters and random anisotropy and reproduces the existence of steps in the magnetizations cycles at very low temperatures. The theoretical results are compared with the experimental data of the very complex magnetic behaviour of CeNi1-xCux alloys. In particular, we can account for the existence of a cluster spin glass state which changes continuously into an inhomogeneous ferromagnetic phase at very low temperatures..

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