  We consider a collisionless ensemble of classical particles coupled to a
Klein-Gordon field. For the resulting nonlinear system of partial differential
equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time
existence of classical solutions and a continuation criterion which says that a
solution can blow up only if the particle momenta become large. We also show
that classical solutions are global in time in the one-dimensional case.
