The human mind can segment continuous streams of activity in the world into meaningful, discrete units known as events. However, not all events are created equal. We draw a distinction between bounded events (e.g., folding a handkerchief) that have a predictable structure that develops in distinct stages (i.e., a beginning, middle, and end) and a well-defined endpoint, and unbounded events (e.g., waving a handkerchief) that lack such a well-defined structure and endpoint. We predict that event boundedness affects attention allocation patterns over the course of the event. Here, we tested this prediction using a dwell time paradigm by measuring the time participants spent on each still frame of an activity. We found that event endpoints attracted increased attention compared to midpoints; importantly, this increase was significantly greater when people viewed bounded events compared to unbounded events. In addition, event endpoints attracted increased attention compared to event beginnings, but this pattern also interacted with event boundedness (Experiment 1). These results replicated even when a linguistic preview of the events was introduced (Experiment 2). We conclude that abstract internal event structure (specifically, event boundedness) affects attention allocation during online event apprehension.