Abstract: We prove that the one-dimensional Euler–Poisson system driven by the Poisson forcing together with the usual γ-law pressure, γ≥1, admits global solutions for a large class of initial data. Thus, the Poisson forcing regularizes the generic finite-time breakdown in the 2×2 p-system. Global regularity is shown to depend on whether or not the initial configuration of the Riemann invariants and density crosses an intrinsic critical threshold.