  In this article we are concerned with the existence and orbital stability of
traveling wave solutions of a general class of nonlocal wave equations: $
u_{tt}-Lu_{xx}=B(\pm |u|^{p-1}u)_{xx}$, $ p>1$. The main characteristic of this
class of equations is the existence of two sources of dispersion, characterized
by two coercive pseudo-differential operators $L$ and $B$. Members of the class
arise as mathematical models for the propagation of dispersive waves in a wide
variety of situations. For instance, all Boussinesq-type equations and the
so-called double-dispersion equation are members of the class. We first
establish the existence of traveling wave solutions to the nonlocal wave
equations considered. We then obtain results on the orbital stability or
instability of traveling waves. For the case $L=I$, corresponding to a class of
Klein-Gordon-type equations, we give an almost complete characterization of the
values of the wave velocity for which the traveling waves are orbitally stable
or unstable by blow-up.
