This paper deals with the problem of Blind Source Separation. Contrary to the vast majority of works, we do not assume the statistical independence between sources and explicitly consider that they are dependent. We introduce three particular types of dependent sources and show that their cumulants have interesting properties. Based on these properties, we investigate the behavior of classical Blind Source Separation algorithms when applied to these sources: depending on the source vector, the separation may be successful or some additionnal indeterminacies can be identified.