Understanding the cognitive and neural processes that underlie human decision making requires the successful prediction of how, but also of when, people choose. Sequential sampling models (SSMs) have greatly advanced the decision sciences by assuming decisions to emerge from a bounded evidence accumulation process so that response times (RTs) become predictable. Here, we demonstrate a difficulty of SSMs that occurs when people are not forced to respond at once but are allowed to sample information sequentially: The decision maker might decide to delay the choice and terminate the accumulation process temporarily, a scenario not accounted for by the standard SSM approach. We developed several SSMs for predicting RTs from two independent samples of an electroencephalography (EEG) and a functional magnetic resonance imaging (fMRI) study. In these studies, participants bought or rejected fictitious stocks based on sequentially presented cues and were free to respond at any time. Standard SSM implementations did not describe RT distributions adequately. However, by adding a mechanism for postponing decisions to the model we obtained an accurate fit to the data. Time-frequency analysis of EEG data revealed alternating states of de- and increasing oscillatory power in beta-band frequencies (14–30 Hz), indicating that responses were repeatedly prepared and inhibited and thus lending further support for the existence of a decision not to decide. Finally, the extended model accounted for the results of an adapted version of our paradigm in which participants had to press a button for sampling more information. Our results show how computational modeling of decisions and RTs support a deeper understanding of the hidden dynamics in cognition.