Abstract
In this paper, we mainly discuss the existence and asymptotic stability of traveling fronts for the nonlocal evolution equations. With the monostable assumption, we obtain that there exists a constant \begin{document}$c^*>0$\end{document} , such that the equation has no traveling fronts for \begin{document}$0 and a traveling front for each c ≥ c*. For \begin{document}$c>c^*$\end{document} , we will further show that the traveling front is globally asymptotic stable and is unique up to translation. If we applied to some differential equations or integro-differential equations, our results recover and/or complement a number of existing ones.
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