Nonequilibrium molecular dynamics (NEMD) Simulations have been performed on 1-methyl-3-ethylimidazolium bis(trifluoromethane)sulfonimide [emim][Ntf(2)] using Lees-Edwards boundary conditions. A range of inverse shear rates corresponding to a fraction of the rotational relaxation time for the slowest relaxing molecular axis of anion and cation to 20 rotational relaxation times (1/20 tau(rot) < (gamma) over dot < 5/tau(rot)) has been investigated. An extrapolation of the shear-rate-dependent viscosity obtained from these simulations to zero shear rate using the empirical three-parameter Carreau equation yielded excellent agreement with the viscosity obtained from equilibrium MD simulations. Based upon the Carreau equation fit to the simulation data, shear-thinning behavior was observed in [emim][Ntf(2)] for all shear rates investigated, implying that Newtonian behavior is observed in [emim][Ntf(2)] only for shear rates significantly lower than the inverse rotational relaxation time. A close resemblance between the apparent time-dependent viscosity extracted from equilibrium MID simulations and the shear-rate-dependent viscosity extracted from NEMD simulations has been found and discussed. MD simulations accurately predicted [emim][Ntf(2)] density, self-diffusion coefficients, heat of vaporization, and lattice parameters for the crystalline phase.