  The contributions of confining as well as nonconfining nonperturbative
self-interactions of stochastic background fields to the shear and bulk
viscosities of the gluon plasma in SU(3) Yang-Mills theory are calculated. The
nonconfining self-interactions change (specifically, diminish) the values of
the shear and bulk viscosities by 15%, that is close to the 17% which the
strength of the nonconfining self-interactions amounts of the full strength of
nonperturbative self-interactions. The ratios to the entropy density of the
obtained nonperturbative contributions to the shear and bulk viscosities are
compared with the results of perturbation theory and the predictions of {\cal
N}=4 SYM.
