Abstract: The nonplanar traveling fronts of reaction-diffusion equations have been attracted a lot of attention and pyramidal traveling fronts for the nonlocal delayed diffusion equation are also established in $\Bbb{R}^{N}$ with $N\geq 3$. In fact, the uniqueness and stability for such $N$-dimensional pyramidal traveling fronts are very interesting problems. The current paper shows that the pyramidal traveling front for the nonlocal delayed diffusion equation in $\Bbb{R}^{3}$ is uniquely determined, which is asymptotically stable when the initial perturbations decay at infinity.

Key words: pyramidal traveling wave solution, reaction-diffusion equation, nonlocal delayed, stability