This paper is concerned with the asymptotic stability of planar waves in reaction-diffusion system on R n , where n 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar waves as t → ∞. The convergence is uniform in R n . Moreover, the stability of planar waves in reaction-diffusion equations with nonlocal delays is also established by transforming the delayed equations into a non-delayed reaction-diffusion system.