Although classically Rapid-Eye Movement (REM) sleep was thought to generate desynchronized activity similar to wakefulness, it was found that some brain regions could express Slow Wave activity (SWA), a pattern which was normally typical of slow-wave sleep. To investigate possible underlying mechanisms, we analyzed experimental recordings and introduced a computational model of mice cerebral cortex in REM sleep. We characterized the patterns of slow-wave activity across somatosensory and motor areas, and found that the most prominent REM-related SWA was present in the primary (S1) and secondary (S2) somatosensory areas, more rarely seen in motor cortex, and absent from prefrontal cortex or hippocampus. The SWA also tended to be synchronized in S1 and S2. We next investigated possible mechanisms by using a computational model of the mouse brain consisting of adaptive Exponential (AdEx) mean-fields connected together according to the mouse connectome. To compare with experimental data, the local field potential was calculated in each mouse brain region. To reproduce the experiments, we had to assume a heterogeneous level of adaptation in different cortical regions during REM sleep. In these conditions, the model reproduced some of the experimental observations in the somato-motor areas and the other cortical areas. We then used the model to test how the presence of SWA affected cortical responsiveness. Indeed, we found that the areas expressing SWA had diminished evoked responses, which may have participated in a diminished responsiveness during REM sleep.