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Aims: We investigate the one-zone SSC model of TeV blazars in the presence ofelectron acceleration. In this picture electrons reach a maximum energy whereacceleration saturates from a combination of synchrotron and inverse Comptonscattering losses. Methods: We solve the spatially averaged kinetic equationswhich describe the simultaneous evolution of particles and photons, obtainingthe multi-wavelength spectrum as a function of time. Results: We apply themodel to the rapid flare of Mrk 501 of July 9, 2005 as this was observed by theMAGIC telescope and obtain the relevant parameters for the pre-flare quasisteady state and the ones during the flare. We show that a hard lag flare canbe obtained with parameters which lie well within the range already acceptedfor this source. Especially the choice of a high value of the Doppler factorseems to be necessary.

On the rapid TeV flaring activity of Markarian 501