The asymptotic or self‐similar behavior of the one‐dimensional two‐stream instability previously observed in numerical simulations is investigated theoretically. The main result, the relation&ngr;d = &ngr;e, implies a principle of maximum dissipation. On the microscopic level it is shown that the quasilinear solution is inconsistent with&ngr;d = &ngr;, and the assumption of an adiabatically growing Bernstein‐Greene‐Kruskal wave cannot explain the observed similarity law. It is proposed that the observed behavior is due to the instability of a Bernstein‐Greene‐Kruskal wave. Suitably chosen simulation computations are performed to demonstrate this concept.