Here we present a mathematical model for the dynamics of oncogenesis control in mature T-cell populations within the blood and lymphatic system. T-cell homeostasis is maintained by clonal competition for trophic niches (survival signals stimulated through interactions with self-antigens bound to major histocompatibility molecules), where a clone is defined as the set of T cells carrying the same antigen specific T-cell receptor (TCR). We analytically derive fitness functions of healthy and leukemic clone variants, respectively, that capture the dependency of the stability of the healthy T-cell pool against leukemic invaders on clonal diversity and kinetic parameters. Similar to the stability of ecosystems with high biodiversity, leukemic mutants are suppressed within polyclonal T-cell populations, i.e., in the presence of a huge number of different TCRs. To the contrary, for a low clonal diversity the leukemic clone variants are able to invade the healthy T-cell pool. The model, therefore, describes the experimentally observed phenomenon that preleukemic clone variants prevail in quasi-monoclonal experimental settings (in mice), whereas in polyclonal settings the healthy TCR variants are able to suppress the outgrowth of tumours. Between the two extremal situations of mono- and polyclonality there exists a range of coexistence of healthy and oncogenic clone variants with moderate fitness (stability) each. A variation of cell cycle times considerably changes the dynamics within this coexistence region. Faster proliferating variants increase their chance to dominate. Finally, a simplified niche variation scheme illustrates a possible mechanism to increase clonal T-cell diversity given a small niche diversity.