Pigeons tracked sinusoidal sequences of interfood intervals (IFIs) by pausing in each interval for a time proportional to the preceding interval. Schedules with either long (30-90 s) or short (5-15 s) values, with variable numbers of cycles and starting phase each day, were tracked about equally well. Tracking was apparently immediate and did not improve across sessions. Experiment 2, in which long and short series were presented on alternate days, showed that tracking on long was more impaired than on short. Experiment 3 showed that occasional presentation of a short IFI in a series of fixed, longer IFIs caused a reduction in waiting time in the next IFI. These effects are evidence for a fast-acting timing mechanism in which waiting time in the IFI N + 1 is strongly determined by the preceding IFI, N. Earlier IFIs have some cumulative effect, but the details remain to be elucidated.