This article deals with the problem of blind source separation in the case of a linear and instantaneous mixture. We first investigate the behavior of known independent component analysis (ICA) methods in the case where the independence assumption is violated: specific dependent sources are introduced and it is shown that, depending on the source vector, the separation may be successful or not. For sources which are a probability mixture of the previous dependent ones and of independent sources, we introduce an extended ICA model. More generally, depending on the value of a hidden latent process at the same time, the unknown components of the linear mixture are assumed either mutually independent or dependent. We propose for this model a separation method which combines: (i) a classical ICA separation performed using the set of samples whose components are conditionally independent, and (ii) a method for estimation of the latent process. The latter task is performed by iterative conditional estimation (ICE). It is an estimation technique in the case of incomplete data, which is particularly appealing because it requires only weak conditions.