The problem of a two‐component, collisionless plasma expansion into vacuum is investigated from the viewpoint of the Vlasov–Poisson model. The set of equations is treated both analytically (through the rescaling transformations) and numerically, using a one‐dimensional Eulerian code. In planar geometry, the rescaling allows to conjecture the existence of a self‐similar expansion over long times. Numerical results subsequently confirm the conjecture and show that the plasma becomes neutral over a smaller and smaller scale. A few thermodynamical properties are studied: the temperature is shown to decrease ast−2; the polytropic relation (d/dt)(pn−&ggr;)=0 (with &ggr;=3) is verified asymptotically via a semianalytical argument. Finally, the same problem is studied in a spherical one‐dimensional geometry. The time‐asymptotic solution is again self‐similar. Numerical simulations show that a non‐neutral, multiple‐layer structure appears, which is proved to be stable over long times.