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In this paper, we are interested in blind source separation methods based on joint-diagonalization of combined sets of "spatial t-f distributions" matrices (STFD). Our aim is to perform source separation with no pre-whitening, thanks to the nonorthogonal joint-diagonalization procedure recently proposed in Yeredor (2002). We also show how such an approach makes it possible to give up the classical hypothesis of independence of sources. The problem is, in fact, reformulated in order to treat the case of even correlated sources. Computer simulations are provided in order to illustrate the effectiveness of the proposed approach and to evaluate its advantages with regard to other techniques.