Hyperspectral unmixing is a blind source separation problem that consists in estimating the reference spectral signa- tures contained in a hyperspectral image, as well as their relative contribution to each pixel according to a given mixture model. In practice, the process is further complexified by the inherent spec- tral variability of the observed scene and the possible presence of outliers. More specifically, multitemporal hyperspectral images, i.e., sequences of hyperspectral images acquired over the same area at different time instants, are likely to simultaneously exhibit mod- erate endmember variability and abrupt spectral changes either due to outliers or to significant time intervals between consecutive acquisitions. Unless properly accounted for, these two perturba- tions can significantly affect the unmixing process. In this context, we propose a new unmixing model for multitemporal hyperspec- tral images accounting for smooth temporal variations, construed as spectral variability, and abrupt spectral changes interpreted as outliers. The proposed hierarchical Bayesian model is inferred us- ing a Markov chain Monte Carlo method allowing the posterior of interest to be sampled and Bayesian estimators to be approxi- mated. A comparison with unmixing techniques from the literature on synthetic and real data allows the interest of the proposed ap- proach to be appreciated.