To comprehend speech sounds, listeners tune in to speech rate information in the proximal (immediately adjacent), distal (non-adjacent), and global context (further removed preceding and following sentences). Effects of global contextual speech rate cues on speech perception have been shown to follow constraints not found for proximal and distal speech rate. Therefore, listeners may process such global cues at distinct time points during word recognition. We conducted a printed-word eye-tracking experiment to compare the time courses of distal and global rate effects. Results indicated that the distal rate effect emerged immediately after target sound presentation, in line with a general-auditory account. The global rate effect, however, arose more than 200 ms later than the distal rate effect, indicating that distal and global context effects involve distinct processing mechanisms. Results are interpreted in a two-stage model of acoustic context effects. This model posits that distal context effects involve very early perceptual processes, while global context effects arise at a later stage, involving cognitive adjustments conditioned by higher-level information.