  Shear viscosity is evaluated within a model of the gluon plasma, which is
based entirely on the stochastic nonperturbative fields. We consider two types
of excitations of such fields, which are characterized by the thermal
correlation lengths ~ 1/(g^2 T) and ~ 1/(g^4 T), where "g" is the
finite-temperature Yang-Mills coupling. Excitations of the first type
correspond to the genuine nonperturbative stochastic Yang-Mills fields, while
excitations of the second type mimic the known result for the shear viscosity
of the perturbative Yang-Mills plasma. We show that the excitations of the
first type produce only an O(g^{10})-correction to this result. Furthermore, a
possible interference between excitations of these two types yields a somewhat
larger, O(g^7), correction to the leading perturbative Yang-Mills result.
  Our analysis is based on the Fourier transformed Euclidean Kubo formula,
which represents an integral equation for the shear spectral density. This
equation is solved by seeking the spectral density in the form of the
Lorentzian Ans\"atze, whose widths are defined by the two thermal correlation
lengths and by their mean value, which corresponds to the said interference
between the two types of excitations. Thus, within one and the same formalism,
we reproduce the known result for the shear viscosity of the perturbative
Yang-Mills plasma, and account for possible nonperturbative corrections to it.
