To study T cell receptors' affinity alloantigen-specific anti-K cytotoxic T-lymphocytes (CTL) were divided on fractions by elution from donor K and third-party macrophage monolayers. The functional activity of CTL was suppressed by anti--Ly2 monoclonal antibodies (mAb), 51-Cr-labelled transformed fibroblasts (L-cells) transferred with the H-2K gene were used as targets. The results demonstrate that primary CTL enriched on third-party macrophage monolayers are the most sensitive to anti-Ly2 mAb. T-cells exhausted on third-party monolayer and then enriched on donor monolayer were resistant to treatment with the mAb. Secondary CTL enriched on donor monolayer were resistant to treatment with anti-Ly2 mAb even should they were not exhausted on third-party monolayer. These results show that Ly2 (CD8) molecule plays an essential role in the interaction of CTL with MHC class I molecule only if T-cell receptor has low affinity.