Saccade stop signal and target step tasks are used to investigate the mechanisms of cognitive control. Performance of these tasks can be explained as the outcome of a race between stochastic go and stop processes. The race model analyses assume that response times (RTs) measured throughout an experimental session are independent samples from stationary stochastic processes. This article demonstrates that RTs are neither independent nor stationary for humans and monkeys performing saccade stopping and target-step tasks. We investigate the consequences that this has on analyses of these data. Nonindependent and nonstationary RTs artificially flatten inhibition functions and account for some of the systematic differences in RTs following different types of trials. However, nonindependent and nonstationary RTs do not bias the estimation of the stop signal RT. These results demonstrate the robustness of the race model to some aspects of nonindependence and nonstationarity and point to useful extensions of the model.