  In this paper we study the effect of the anisotropic stress generated by
neutrinos on the propagation of primordial cosmological gravitational waves.
The presence of anisotropic stress, like the one generated by free-streaming
neutrinos, partially absorbs the gravitational waves (GWs) propagating across
the Universe. We find that in the standard case of three neutrino families, 22%
of the intensity of the wave is absorbed, in fair agreement with previous
studies. We have also calculated the maximum possible amount of damping,
corresponding to the case of a flat Universe completely dominated by
ultrarelativistic collisionless particles. In this case 43% of the intensity of
the wave is absorbed. Finally, we have taken into account the effect of
collisions, using a simple form for the collision term parameterized by the
mean time between interactions, that allows to go smoothly from the case of a
tigthly-coupled fluid to that of a collisionless gas. The dependence of the
absorption on the neutrino energy density and on the effectiveness of the
interactions opens the interesting possibility of observing spectral features
related to particular events in the thermal history of the Universe, like
neutrino decoupling and electron-positron annihilation, both occurring at T~1
MeV. GWs entering the horizon at that time will have today a frequency $\nu\sim
10^{-9} \Hz$, a region that is going to be probed by Pulsar Timing Arrays.
