The vertebrate immune system is able to detect abnormal body cells by the specific repertoire of 8 - 12 residues long peptides (= epitopes or peptide antigens) presented at the cell surface by the MHC-1 molecule complex. The generation of an epitope starts with the degradation of endogenous proteins into primary oligomeric fragments by cytosolic proteases, predominantly the proteasome. These primary fragments may be further attacked by various amino peptidases resident in the cytosol or, alternatively, may escape from this attack by entering the endoplasmic reticulum (ER) by the transporter associated with antigen presentation (TAP). To study the possible consequences of this scenario for the efficiency of antigen presentation we have applied kinetic modelling. The mathematical model comprises the generation of primary oligomeric fragments containing the definitive epitope, the successive N-terminal shortening of these primary fragments by cytosolic amino peptidases and the TAP-mediated transport of cytosolic peptides into the ER. Because the number of peptide molecules may become very small we have performed deterministic and stochastic simulations of the kinetic model. Our simulations show that cytosolic N-terminal trimming of primary fragments may drastically increase loading epitope precursors into the ER. In particular, a primary fragment generated with a low rate of TAP transport into the ER may nevertheless become a potent epitope precursor if at least one of its N-terminal trimming products will be efficiently transported.