The coexistence between a strained crystal and its shearing melt is studied using nonequilibrium molecular dynamics simulations of Lennard-Jones particles. The coexistence is found to be independent of initial conditions, boundary effects, and the details of the thermostat. The nonequilibrium phase diagram is presented. The shear stress at coexistence is found to be significantly smaller than the yield stress of the crystal. It is demonstrated that there exists no physically reasonable prescription for a nonequilibrium analogue of chemical potential for the shearing liquid by which the coexistence could be attributed to an equality of chemical potentials between the two phases. We conclude that the nonequilibrium coexistence is determined by the stability of the interface. (C) 2003 American Institute of Physics.