This paper is concerned with the problem of separating independent non‐Gaussian sources. This is done by adaptively maximizing a contrast function based on fourth‐order cumulants of the (mixed) obser$softhyphen;vations. The first cla ss of solutions involves a first stage where the signal vector is adaptively whitened. In order to implement in the second stage the proper separating task, new contrast functions are proposed, especially when all the source kurtosises have the same sign. These contrasts involve only self‐cumulants of the outputs. The second class of solutions requires a single separating stage. However, the associated contrasts involve cross‐cumulants in addition to self‐cumulants. They essentially apply to correlated ve ctors with normalized powers (rather than to white vectors). The resulting adaptive one‐stage and two‐stage systems achieve satisfactory separation performance independently of the statistics of sources and of the kind of linear mixture.