This paper considers change detection with multitemporal synthetic aperture radar (SAR) images. A novel statistical approach is developed that formulates the detection of changes between two coregistered SAR images acquired at different dates as a non-parametric local-window hypothesis testing problem. This approach takes into account the simultaneous testing of a large amount of similar hypotheses (i.e., one Wilcoxon test at each pixel of the image), and is based on a likelihood ratio test to obtain a detection map at the pixel level. Some encouraging detection results are obtained on XSAR and very high resolution COSMO-SkyMed images.