Adaptive methods are commonly used in psychophysical research for detection and discrimination (see Leek, 2001; Treutwein, 1995, for reviews). In recent years, researchers have investigated via simulations some asymptotic and small-sample properties of two nonparametric adaptive methods-namely, the fixed-step-size up-down (García-Pérez, 1998, 2001) and the (accelerated) stochastic approximation (Faes et al., 2007). In the present article, we extend both methods to the simple reaction time (RT) situation for the measure of signal intensities that elicit certain (fixed) RT percentiles. We focus on extending the following four methods: the stochastic approximation of Robbins and Monro (1951), its accelerated version of Kesten (1958), the transformed up-down of Wetherill (1963), and the "biased coin design" of Durham and Flournoy (1994, 1995). In all simulations, we assume that the RT is Weibull distributed and that there is a linear relationship between the mean RT and its standard deviation. The convergences of the asymptotic and small-sample properties for different starting values, step sizes, and response criteria are systematically investigated.