Two new Bayesian Maximum A Posteriori (MAP) vector speckle filters are developed for multi-channel detected SAR images. These filters incorporate statistical descriptions of the scene and of the speckle in multi-channel SAR images. These models account for the scene and system effects which result in the presence of a certain amount of correlation between the different channels. In order to account for the effects due to the spatial correlation of both the speckle and the scene in SAR images, estimators originating from the local autocorrelation functions are incorporated to these filters, to refine the evaluation of the non-stationary first order local statistics, as well as to improve the restoration of the scene textural properties and to preserve the useful spatial resolution in the speckle filtered image. Results obtained, first on 3-look spaceborne ERS PRI multi-temporal images, then on a couple of ERS PRI and RADARSAT standard beam SAR images illustrate the performance of these estimators for different SAR combinations. These results show that these filters present convincing performances for speckle reduction, as well as for texture preservation and for small and/or thin scene objects detection. Finally, since the new established Bayesian speckle filters present the structure of control systems, promising perspectives are presented for the development of application oriented processing chains for multi-channel SAR images, where the speckle filtering operation will be the first processing step.