Context : We present the first dynamical study of the globular cluster system of NGC 4636 .
It is the southernmost giant elliptical galaxy of the Virgo cluster , and is claimed to be extremely dark matter dominated , according to X–ray observations .

Aims : Globular clusters are used as dynamical tracers to investigate , by stellar dynamical means , the dark matter content of this galaxy .

Methods : Several hundred medium resolution spectra were acquired at the VLT with FORS 2/MXU .
We obtained velocities for 174 globular clusters in the radial range 0 { \mbox { $ . ^ { \prime } $ } } 90 < R < 15 { \mbox { $ . ^ { \prime } $ } } 5 , or 0.5 -9 R _ { e } in units of effective radius .
Assuming a distance of 15 Mpc , the clusters are found at projected galactocentric distances in the range 4 to 70 kpc , the overwhelming majority within 30 kpc .
The measured line–of–sight velocity dispersions are compared to Jeans–models .

Results : We find some indication for a rotation of the red ( metal-rich ) clusters about the minor axis .
Out to a radius of 30 kpc , we find a roughly constant projected velocity dispersion for the blue clusters of \sigma \approx 200 \textrm { km s } ^ { -1 } .
The red clusters are found to have a distinctly different behavior : at a radius of about 3 ^ { \prime } , the velocity dispersion drops by \sim 50 \textrm { km s } ^ { -1 } to about 170 \textrm { km s } ^ { -1 } which then remains constant out to a radius of 7 ^ { \prime } .
The cause might be the steepening of the number density profile at \sim 3 { \mbox { $ { } ^ { \prime } $ } } observed for the red clusters .
Using only the blue clusters as dynamical tracers , we perform Jeans-analyses for different assumptions of the orbital anisotropy .
Enforcing the model dark halos to be of the NFW type we determine their structural parameters .
Depending on the anisotropy and the adopted M/L-values , we find that the dark matter fraction within one effective radius can vary between 20 % and 50 % with most a probable range between 20 % and 30 % .
A main source of uncertainty is the ambiguity of the velocity dispersion in the outermost bin .
A comparison with cosmological N–body simulations reveals no striking disagreement .

Conclusions : Although the dark halo mass still can not be strongly constrained , NGC 4636 does not seem to be extremely dark matter dominated .
The derived circular velocities are also consistent with Modified Newtonian Dynamics .