  We present first elements of kinetic theory appropriate to the inhomogeneous
phase of the HMF model. In particular, we investigate the case of strongly
inhomogeneous distributions for $T\to 0$ and exhibit curious behaviour of the
force auto-correlation function and friction coefficient. The temporal
correlation function of the force has an oscillatory behaviour which averages
to zero over a period. By contrast, the effects of friction accumulate with
time and the friction coefficient does not satisfy the Einstein relation. On
the contrary, it presents the peculiarity to increase linearly with time.
Motivated by this result, we provide analytical solutions of a simplified
kinetic equation with a time dependent friction. Analogies with
self-gravitating systems and other systems with long-range interactions are
also mentioned.
