Blind source separation refers to the inferring of the values of variables (known as sources) from observations that are linear combinations of them. The observations and sources are usually vectors. Both the sources and the matrix of linear coefficients may be unknown. Here we describe an approach where the sources are assumed to be Gaussian mixtures. An MCMC procedure has been developed that computes the posterior distribution of sources and the matrix of linear coefficients from observations. It is applied to source separation in multi-channel extra-terrestrial microwave data, with the goal of separating out the cosmic microwave background signal.