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The aim of this paper is to prove stability of traveling waves forintegro-differential equations connected with branching Markov processes. Inother words, the limiting law of the left-most particle of a (time-continuous)branching Markov process with a L\'{e}vy non-branching part is demonstrated.The key idea is to approximate the branching Markov process by a branchingrandom walk and apply the result of A\"{i}d\'{e}kon [1] on the limiting law ofthe latter one.

On stability of traveling wave solutions for integro-differential equations related to branching Markov processes