The exact master equation of Prigogine and Re´sibois is derived for inhomogeneous as well as homogeneous systems. The asymptotic master equation is obtained from the following postulate: The singularities of the analytically continued Liouville resolvent nearest the real axis are isolated simple poles arising from “irreducible vacuum‐to‐vacuum” transitions. The asymptotic distribution function found in this way differs from the one obtained previously. If the asymptotic distribution function at time t1, fa(t1) is taken as a new initial value in the exact master equation, and the subsequent asymptotic solution is calculated for a time t2later, the result is fa(t1 + t2).