In the antisaccade task participants are required to saccade in the opposite direction of a peripheral visual cue (PVC). This paradigm is often used to investigate inhibition of reflexive responses as well as voluntary response generation. However, it is not clear to what extent different versions of this task probe the same underlying processes. Here, we explored with the Stochastic Early Reaction, Inhibition, and late Action (SERIA) model how the delay between task cue and PVC affects reaction time (RT) and error rate (ER) when pro- and antisaccade trials are randomly interleaved. Specifically, we contrasted a condition in which the task cue is presented prior to the PVC with a condition in which the PVC serves also as task cue. Summary statistics indicate that ER and RTs are reduced and contextual effects largely removed when the task is signaled before the PVC appears. The SERIA model accounts for RT and ER in both conditions, and better so than other candidate models. Modeling demonstrates that voluntary pro- and antisaccades are frequent in both conditions. Moreover, early task cue presentation results in better control of reflexive saccades leading to fewer fast antisaccade errors and more rapid correct prosaccades. Finally, high latency errors are shown to be prevalent in both conditions. In summary, SERIA provides an explanation for the differences in the delayed and non-delayed antisaccade task.