Using an identical pair of passively mode-locked fiber lasers, we demonstrate a new method of temporal scanning by periodically varying the cavity length of one laser. This scanning temporal ultrafast delay (STUD) technique produces scanning performance far exceeding that obtainable with conventional, mechanical scanning: For a pair of 5-MHz lasers, we obtain a scan range of Delta T = 10 ns at a scan frequency of f(scan) = 25 Hz; and for 50-MHz lasers, we obtain Delta T = 5 ns at f(scan) = 100 Hz. Highly accurate timing calibration is obtained by using multiple-pulse cross correlations. We use this method to characterize the timing jitter between the two lasers while they are scanning, and the reproducibility of the scanning. Timing accuracy of 200 fs over a 300-ps scan range is obtained for individual scans. Finally, we demonstrate the utility of this technique by using the dual laser system io measure carrier lifetimes in samples of ion-bombarded and intrinsic InGaAs. The selectability of the sweep rate and the scan range along with the subpicosecond accuracy give this technique a large temporal dynamic range, resembling the functionality of oscilloscopes.