  We investigate the molecular gas content and the excitation and fragmentation
properties in the central region of the spiral galaxy Messier 81 in both the
^{12}CO(1-0) and ^{12}CO(2-1) transitions. We have recently observed the two
transitions of CO in the M~81 center with A, B, and HERA receivers of the IRAM
30-m telescope. We find no CO emission in the inner $\sim$ 300 pc and a weak
molecular gas clump structure at a distance of around 460 pc from the nucleus.
Observations of the first two CO transitions allowed us to compute the line
ratio, and the average I_{21}/I_{10} ratio is 0.68 for the M~81 center. This
low value, atypical both of the galactic nuclei of spiral galaxies and of
interacting systems, is probably associated to diffuse gas with molecular
hydrogen density that is not high enough to excite the CO molecules. After
analyzing the clumping properties of the molecular gas in detail, we identify
very massive giant molecular associations (GMAs) in CO(2-1) emission with
masses of $\sim$ 10$^{5}$ M$_\odot$ and diameters of $\sim$ 250 pc. The deduced
N(H_{2})/I_{CO} ratio for the individually resolved GMAs, assumed to be
virialized, is a factor of $\sim$ 15 higher than the \textit{standard} Galactic
value, showing - as suspected - that the X ratio departs significantly from the
mean for galaxies with an unusual physics of the molecular gas.
