We describe a new nonequilibrium molecular dynamics algorithm for simulating multicomponent diffusion within the Stefan-Maxwell framework. The approach developed here allows for the efficient computation of a full diffusion-coefficient matrix for solutions containing any number of species. Due to our interest in electrolytes, the method is tested by simulating aqueous KCl and NaCl salt solutions in the concentration range 1-4 m. The results are in semiquantitative agreement with experiment and in quantitative agreement with previous Green-Kubo calculations for our potential models. This provides strong evidence that the equilibrium and nonequilibrium methods are correct.