T-cell receptor (TCR) polyclonal mature T cells are surprisingly resistant to oncogenic transformation after retroviral insertion of T-cell oncogenes. In a mouse model, it has been shown that mature T-cell lymphoma/leukemia (MTCLL) is not induced upon transplantation of mature, TCR polyclonal wild-type (WT) T cells, transduced with gammaretroviral vectors encoding potent T-cell oncogenes, into RAG1-deficient recipients. However, further studies demonstrated that quasi-monoclonal T cells treated with the same protocol readily induced MTCLL in the recipient mice. It has been hypothesized that in the TCR polyclonal situation, outgrowth of preleukemic cells and subsequent conversion to overt malignancy is suppressed through regulation of clonal abundances on a per-clone basis due to interactions between TCRs and self-peptide-MHC-complexes (spMHCs), while these mechanisms fail in the quasi-monoclonal situation. To quantitatively study this hypothesis, we applied a mathematical modeling approach. In particular, we developed a novel ordinary differential equation model of T-cell homeostasis, in which T-cell fate depends on spMHC-TCR-interaction-triggered stimulatory signals from antigen-presenting cells (APCs). Based on our mathematical modeling approach, we identified parameter configurations of our model, which consistently explain the observed phenomena. Our results suggest that the preleukemic cells are less competent than healthy competitor cells in acquiring survival stimuli from APCs, but that proliferation of these preleukemic cells is less dependent on survival stimuli from APCs. These predictions now call for experimental validation.