Molecular-dynamics simulations have been employed to calculate the coefficients of shear and bulk viscosity of a Lennard-Jones liquid in the temperature range T* = 0.4-2.0 in stable and metastable states. Penetration into the region of superheated states, as distinct from supercooled ones, does not lead to any essential changes in the shear viscosity. The bulk viscosity increases at the approach to the lines of liquid-crystal and liquid-gas equilibrium and in the metastable states. The evolution of autocorrelation functions of the components of the pressure tensor and the characteristic times of the viscoelastic relaxation of both a superheated and supercooled liquids has been investigated. (C) 2011 Elsevier B.V. All rights reserved.