A one-parameter model constitutive transport equation for the viscosity of the Lennard-Jones (L-J) fluid that is accurate for all equilibrium states of liquid and gas is proposed: eta(rho*, T*) = eta(0)(T*)[1 + B-eta(*)(T*)rho* + C-AH(1/T*)(1/3)(rho*)(4)] The form of this equation is based upon the soft-sphere scaling laws for the residual density-dependent viscosity discovered originally by Ashurst and Hoover and uses their empirical coefficient (C-AH). Enskog's density-independent limit theoretical term (eta(0)) is included to reproduce the viscosity in the limit of zero density accurately. Remaining discrepancies at low temperatures, for both gas and liquid densities, are largely removed when the linear-density Rainwater-Friend coefficient is added. The equation is comparable in accuracy to the 24-parameter empirical equation of state proposed by Rowley and Painter. Comparison with this correlation and previous MD results reveals a discrepancy near the triple point. To test the equation, new MD data for three fluid states are reported. Here, the viscosity is computed from time correlation functions resolved into the single-particle auto- and cross-correlation terms. It is found that, at high density (rho* > 0.8), the cross-correlations extend beyond 7 sigma, (molecule diameters) and oscillate in sign. This explains the wide scatter of previous MD viscosities for small L-J systems. (c) 2005 American Institute of Chemical Engineers AIChE J, 52: 438-446, 2006