Resumen
By using Schauder's fixed point theorem, we prove some existence results for traveling wavefronts of reaction-diffusion systems with quasimonotonicity reactions. More precisely, we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice. Finally, to illustrate our main results, we study the existence of traveling wavefronts for a delayed predator-prey model with diffusion as well as the reaction-diffusion system with the well-known Belousov-Zhabotinskii reaction, and the obtained results improve the existing ones.