Two experiments used response-initiated delay schedules to test the idea that when food reinforcement is available at regular intervals, the time an animal waits before its first operant response (waiting time) is proportional to the immediately preceding interfood interval (linear waiting; Wynne & Staddon, 1988). In Experiment 1 the interfood intervals varied from cycle to cycle according to one of four sinusoidal sequences with different amounts of added noise. Waiting times tracked the input cycle in a way which showed that they were affected by interfood intervals earlier than the immediately preceding one. In Experiment 2 different patterns of long and short interfood intervals were presented, and the results implied that waiting times are disproportionately influenced by the shortest of recent interfood intervals. A model based on this idea is shown to account for a wide range of results on the dynamics of timing behavior.