T lymphocytes expressing alpha beta T-cell receptors with sufficient affinity to major histocompatibility complex (MHC) molecules expressed on thymus epithelial cells are positively selected and mature to functional T cells. But several studies have demonstrated that athymic nude mice grafted with MHC-incompatible thymuses developed T cells specific for nude host rather than thymic MHC. We examined this paradox by analysing the specificity of T lymphocytes derived from nude mice. We report here that nude T lymphocyte precursors transferred to allogeneic SCID (severe combined immunodeficiency) mice with a functioning thymus (but lacking T or B cells) generated host MHC-restricted effector T cells but also contained T cells restricted to donor MHC. If nude T cells were depleted from nude lymphohaemopoietic donor cells before or after transfer, only host MHC-specific T cells matured. The results may explain the unusual MHC specificities of nude T lymphocytes described in earlier studies and demonstrate two separate differentiation steps: in nude mice, T cells may be positively selected for self-MHC restriction specificity extrathymically; then a functional thymus is required for efficient T cell maturation.