The broad-band SEDs of blazars exhibit two broad spectral components, which in leptonic emission models are attributed to synchrotron radiation and synchrotron self-Compton (SSC) radiation of relativistic electrons. During high-state phases, the high-frequency SSC component often dominates the low-frequency synchrotron component, implying that the inverse-Compton SSC losses of electrons are at least equal to or greater than the synchrotron losses of electrons. We calculate from the analytical solution of the kinetic equation of relativistic electrons, subject to the combined linear synchrotron and non-linear SSC cooling, for monoenergetic injection the time-integrated total synchrotron and SSC radiation fluences and spectral energy distributions (SEDs). Depending on the ratio of the initial cooling terms, displayed by the injection parameter α, we find for α≪ 1, implying complete linear cooling, that the synchrotron peak dominates the inverse-Compton peak and the usual results of the spectra are recovered. For α≫ 1, the SSC peak dominates the synchrotron peak, proving our assumption that in such a case the cooling becomes initially non-linear. The spectra also show some unique features, which can be attributed directly to the non-linear cooling. To show the potential of the model, we apply it to outbursts of 3C 279 and 3C 454.3, successfully reproducing the SEDs. The results of our analysis are promising, and we argue that this non-equilibrium model should be considered in future modelling attempts for blazar flares.