This paper studied Bayesian algorithms for separating linear mixtures of spectral sources under non-negativity and full additivity constraints. These two constraints are required in some applications such as hyperspectral imaging and spectroscopy to get meaningful solutions. A hierarchical Bayesian model was defined based on priors ensuring the fulfillment of the constraints. Estimation of the sources as well as the mixing coefficients was then performed by using samples distributed according to the joint posterior distribution of the unknown model parameters. A Gibbs sampler strategy was proposed to generate samples distributed according to the posterior of interest. The generated samples were then used to estimate the unknown parameters. The performance of the algorithm was first illustrated by means of simulations conducted on synthetic signals. The application to the separation of chemical mixtures resulting from Raman spectroscopy was finally investigated. The proposed Bayesian algorithm provided very promising results for this application. Particularly, when the computational times is not a study constraint, the proposed method clearly outperforms other standard NMF techniques, which can give approximative solutions faster. Perspectives include the development of a similar methodology for unmixing hyperspectral images. Some results were already obtained for the unmixing of known sources. However, the joint estimation of the mixing coefficients (abundances) and the sources (endmembers) is a still an open and challenging problem.