The case of a slightly anharmonic oscillator (with a βx4 perturbing potential) is examined in the framework of stochastic electrodynamics (SED) in full detail. We obtain the stationary probability density and the mean energy, which differs from the quantum result at order β2. Using Kubo’s linear response theory we obtain the absorption curve: the maximum absorption frequencies do not coincide with the quantum transition frequencies. From the calculation of the emission energy we show that the ’’radiation balance’’ is not exactly satisfied as soon as β≠0, a property which disagrees with the quantum results. Finally, we discuss the consequences of this lack of radiation balance concerning Kirchhoff’s law.