  The aim of this paper is to prove stability of traveling waves for
integro-differential equations connected with branching Markov processes. In
other 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 branching
random walk and apply the result of A\"{i}d\'{e}kon [1] on the limiting law of
the latter one.
