\Ve have developed a nonequilibrium molecular dynamic method to directl), simulate dense fluid transport (Ashurst and Hoover, 1975). The trajectories of N interacting atoms in a £i.,ed volume V are numerically computed. External forces, which are restricted to special boundary regions, do work and extract heat in order to maintain the hydro dynamic boundary conditions which produce a steady shear-momentum or heat flux. The transport coefficient is deternlined from the time average of the flux and corre sponding gradient in the volume V . . Experimental observation of dense fluid shear viscosity and thermal conductivity data reveals that the excess co efficient, that part above the temperature-dependent dilute gas value, is almost temperature independent (Diller et aI., 1970; Hanley et al., 1972). In order to calculate repre sentative dense fluid transport coefficients, we have se lected the Lennard-Jones potential (twelfth-power repul sion with sixth-power attraction) as a simple, yet realistic, atomic potential. Mos.t atomic interactions occur with en .ergy of order kT; thus, for high temperatures, the Lennard' Jones potential is effectively a single inverse power poten tiaL The single inverse nth power potentials have special scaling features since the potential and its derivatives de pend only upon the combination of energy and particle size feTn. Thus, if the density and temperature are com bined into one variable x [== (density) (temperature) -Un], then all svstems with identical scaled initial conditions and the same' x value will have identical dynamic evolution (Hoover et aI., 1971). The reduced excess transport coeffi cients times (dkT) 1/2+2/11 are functions of x only, not density and temperature separately, throughout the £uid phase. Since, at high teD,lperature, the repulsive core potential dominates momentum transport, the high-temperature Lennard-Jones shear viscosity must approach the scaling behavior of the inverse-12th-power viscosity. I\'onequilib rium molecular dynamic calculations for the Lennard-Jones shear viscosity have shown this to be true and we have found that the scaling is sllccessful even at the triple point (Nc?/V :::: 0.8.5, kTh = 0,70). The LenHard-Jolles shear viscosity has been calculated (with 108 and 216 atoms) along two isotherms co~respondillg to room temperature forhvdrogen and helium (kT/ f :::: 3.5 and 28) for densi , ~ [ , ( ,,' , / 1 I 1 Th tieS up to reezmg \1, rr , = ,0 i, see ·lgllre. 8 cnlcubted redl;cPci excess shear viscosity A'l) for x > ....0.5 is well descrikJ by the simple expression