  The Nordstr\"om-Vlasov system is a Lorentz invariant model for a
self-gravitating collisionless gas. We establish suitable a-priori-bounds on
the solutions of this system, which together with energy estimates and the
smoothing effect of ``momentum averaging'' yield the existence of global weak
solutions to the corresponding initial value problem. In the process we improve
the continuation criterion for classical solutions which was derived recently.
The weak solutions are shown to preserve mass.
