In a homogeneous plasma with no external fields, an equation of evolution for the space‐averaged distribution f¯ (v,t) is derived without making use of the Markovian approximation. The Vlasov equation is integrated for a limited, albeit arbitrary, time interval along analytical particle orbits. Orbit failure is avoided by considering a sequence of initial value problems. A Markovian limit is identified, in which quasilinear, resonance broadening, and mode coupling theories are recovered. Under non‐Markovian conditions, the quasilinear wave–particle resonance is broadened at orderE2.