The nonlocal shear viscosity n(t) of a classical one-component plasma is shown to have anoscillatory long-time tail. This result is obtained on the basis of amicroscopic theory which does not rely on expansions in a small parameter such as the plasma expansion parameter. Our major approximation is the restriction to the coupling oftwo hydrodynamic propagators in the computation of the long-time behavior of the transport matrix. The Coulomb divergence is correctly accounted for, while the nonanalyticities of both the plasma parameter and gradient expansions are discussed at the level of the kinetic as well as the hydrodynamic equations.