Triggering of the T cell receptor (TCR) may be antagonized by ligands that are slight variants of the immunogenic peptide. This paper proposes a mathematical model to quantify the strength of the antagonistic effect. The model is based on the kinetics of association and dissociation of TCR and peptide/major histocompatibility (pMHC) molecules, and incorporates TCR triggering according to a kinetic proofreading mechanism. Model analysis indicates that while the average lifetime of the TCR/pMHC complex is the basic determinant of the contribution to TCR triggering made by the ligand, the affinity of the ligand and its MHC presentation level are also important. However, these contributions depend on the kinetic limitation regime. There is a continuum of limitation regimes, at the extremes of which are found TCR limitation and MHC limitation. Both ligand affinity and TCR and pMHC densities determine whether TCR triggering is TCR limited or MHC limited. The changing importance of affinity and antigen presentation level under various kinetic limitation regimes may explain the respective roles of antagonistic and agonistic self peptides in thymic selection. Moreover, TCR down-regulation under TCR-limited conditions may allow the T cell to differentiate between the average lifetime of the TCR/pMHC complex and the presentation level of the ligand. A method for experimental differentiation between passive and active antagonistic effects is proposed which exploits the differences between TCR and MHC limitation.