Two experiments studied the emergence of bindings between stimulus features (object files) and between stimulus and response features (event files) over time. Choice responses (R2) were signalled by the shape of a stimulus (S2) that followed another stimulus (S1) of the same or different shape, location, and colour. S1 did not require a response (Experiment 1) or trigger a precued simple response (R1) that was or was not repeated by R2 (Experiment 2). Results demonstrate that the mere cooccurrence of stimulus features, and of stimuli and responses, is sufficient to bind their codes. Bindings emerge quickly and remain intact for at least four seconds. Which features are considered depends on their task‐relevance; hence, integration reflects the current attentional set. There was no consistent trend toward higher order interactions as a function of time or of the amount of attention devoted to S1, suggesting that features are not integrated into a single, global superstructure, but enter independent local bindings presumably subserving different functions.