Abstract: We present high-resolution HIFI spectroscopy of the nucleus of the archetypical starburst galaxy M 82. Six 12CO lines, 2 13CO lines and 4 fine-structure lines have been detected. Besides showing the effects of the overall velocity structure of the nuclear region, the line profiles also indicate the presence of multiple components with different optical depths, temperatures, and densities in the observing beam. The data have been interpreted using a grid of PDR models. It is found that the majority of the molecular gas is in low density (n = 103.5 cm-3) clouds, with column densities of NH = 1021.5 cm-2 and a relatively low UV radiation field (G0 = 102). The remaining gas is predominantly found in clouds with higher densities (n = 105 cm-3) and radiation fields (G0 = 102.75), but somewhat lower column densities (NH = 1021.2 cm-2). The highest J CO lines are dominated by a small (1% relative surface filling) component, with an even higher density (n = 106 cm-3) and UV field (G0 = 103.25). These results show the strength of multi-component modelling for interpretating the integrated properties of galaxies.