Classical solutions of the spherically symmetric Nordström–Vlasov system are shown to exist globally in time. The main motivation for investigating the mathematical properties of the Nordström–Vlasov system is its relation to the Einstein–Vlasov system. The former is not a physically correct model, but it is expected to capture some of the typical features of the latter, which constitutes a physically satisfactory, relativistic model but is mathematically much more complex. We show that classical solutions of the spherically symmetric Nordström–Vlasov system exist globally in time for compactly supported initial data under the additional condition that there is a lower bound on the modulus of the angular momentum of the initial particle system. We emphasize that this is not a smallness condition and that our result holds for arbitrary large initial data satisfying this hypothesis.