Nasal breathing generates a rhythmic signal which entrains cortical network oscillations in widespread brain regions on a cycle-to-cycle time scale. It is unknown, however, how respiration and neuronal network activity interact on a larger time scale: are breathing frequency and typical neuronal oscillation patterns correlated? Is there any directionality or temporal relationship? To address these questions, we recorded field potentials from the posterior parietal cortex of mice together with respiration during REM sleep. In this state, the parietal cortex exhibits prominent theta and gamma oscillations while behavioral activity is minimal, reducing confounding signals. We found that the instantaneous breathing frequency strongly correlates with the instantaneous frequency and amplitude of both theta and gamma oscillations. Cross-correlograms and Granger causality revealed specific directionalities for different rhythms: changes in theta activity precede and Granger-cause changes in breathing frequency, su...