  We study local well-posedness and orbital stability/instability of standing
waves for a first order system associated with a nonlinear Klein-Gordon
equation on a star graph. The proof of the well-posedness uses a classical
fixed point argument and the Hille-Yosida theorem. Stability study relies on
the linearization approach and recent results for the NLS equation with the
$\delta$-interaction on a star graph.
