Introduces self-adaptive algorithms for source separation based on a generalized criterion with the introduction of cross-cumulants. By adequate adaptive preprocessing it can be supposed that the observed source mixture x is 'white'. Then a separating matrix H (such that y=Hx has independent components) can be assumed unitary. A new contrast function is defined whose maximum occurs when H is separating. Its (simple) form admits an associated adaptive algorithm. Two different algorithms are proposed to estimate H, either directly or through its equivalent product of Givens rotations. Computer simulations illustrate the contribution of the cross-cumulants on the convergence of the algorithms. In the three-sources case, they show that the performances are improved substantially.< >