2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/14212The recent detection of high energy gamma-rays coming from supernova remnants and active galactic nuclei has revived interest in the diffusive shock acceleration of electrons. In the present paper we examine the basis of the so-called ``box'' model for particle acceleration and present a more physical version of it. Using this we determine simple criteria for the conditions under which ``pile-ups'' can occur in shock accelerated electron spectra subject to synchrotron or inverse Compton losses (the latter in the Thompson limit). An extension to include nonlinear effects is proposed.6 pages, 3 figures, accepted for publication in Astronomy and AstrophysicsAstrophysicstext