Two models are presented for the response times of different operators to different tasks where response is initiated by one or more cues provided by the system. One model for the log-response times is a mixed or latent factor model with unequal case fixed effects and variances. The other model for the log-response times is a non-Gaussian log-extreme-value model. Procedures for estimating the parameters by maximum likelihood are presented. The models are used to analyze response time data from simulator experiments involving nuclear power plant operators performing certain safety-related tasks. The findings of the models are critiqued and applications to risk analysis are sketched. Keyword: Extreme-value distribution; Weibull distribution. (KR)