The solid-liquid equilibrium phase transition of a one-component Lennard-Jones system is determined by equilibrium and nonequilibrium molecular dynamics simulation methods. One method uses the observation that the scaling exponent of the pressure or energy of a shearing Lennard-Jones liquid is approximately 1 at the solid phase. This enables us to locate the density of the coexisting solid phase. The coexisting liquid phase density is then obtained by constructing a tie line between the coexisting solid phase point and the liquid phase curve. Alternatively, the coexisting liquid phase density can be efficiently obtained by observing the change in pressure as a function of strain rate and density. The coexisting solid phase density can be then obtained from a tie line from the liquid curve to the solid curve. These calculations are the first reported use of combined equilibrium and nonequilibrium molecular dynamics methods for phase coexistence at equilibrium. Our results are in very good agreement with those obtained by alternative simulation methods for phase equilibria. (C) 2003 American Institute of Physics.