The ac power flow in an electron beam moving in weak electric fields is given a precise definition. Since it is a quantity quadratic in the applied field strength its evaluation requires the quadratic perturbation theory of the beam to be worked out. Quadratic expressions in the first‐order variables of the beam and circuit may also be written down which have the dimensions of power and are shown to satisfy a conservation theorem. The relations between the exact quantities of the nonlinear theory and the constructs from linear theory are discussed.