That HIV-specific cytotoxic T-lymphocytes (CTLs) might be defective in some way has stimulated much controversy and research. We use mathematical models to explore the predictions of two competing CTL-defect theories: ''defective memory'' and ''defective activation''. We discuss whether these models are consistent with adoptive-transfer experiments in HIV-infected patients and vaccine trials in simian immunodeficiency virus (SIV)-infected monkeys. Finally, we describe experimental tests that could decide among these two theories and a competitor: CTL exhaustion.